Patent Grant
7526053
1. Field of the Invention
This invention relates to digital communication systems and, more particularly, to a detection system and method for an Ethernet receiver.
2. Discussion of Related Art
The dramatic increase in desktop computing power driven by Intranet-based operations and the increased demand for time-sensitive delivery between users has spurred development of high-speed Ethernet LANs. 100BASE-TX Ethernet, using existing category-5 copper wire, and the newly developed 1000BASE-T Ethernet for gigabit per second (gigabit/s) transfer of data over category-5 copper wire require new techniques in high speed symbol processing. Gigabit/s transfer can be accomplished utilizing four twisted pairs and a 125 megasymbol per second (megasymbol/s) transfer rate on each pair where each symbol represents two bits.
Physically, data is transferred using a set of voltages where each voltage represents one or more bits of data. Each voltage in the set is referred to as a symbol and the whole set of voltages is referred to as a symbol alphabet. In gigabit/s transfer, for example, data is usually sent with a set of five voltage levels (PAM-5), each symbol representing two bits.
One system of transferring data at high rates is non-return-to-zero (NRZ) signaling. In NRZ, the symbol alphabet {A} is {−1, +1}. A logical “1” is transmitted as a positive voltage while a logical “0” is transmitted as a negative voltage. At 125 megasymbols/s, the symbol rate required for gigabit/s transfer over four category-5 wires, the pulse width of each symbol is 8 ns.
Another example of a modulation method for high speed symbol transfer is multilevel transmission-3 (MLT-3) encoding and involves a three-level system. (See American National Standard Information System, Fibre Distributed Data Interface (FDDI)-Part: Token Ring Twisted Pair Physical Layer Medium Dependent (TP-PMD), ANSI X3.263:199X.) The symbol alphabet {A} for MLT-3 is {−1, 0, +1}. In MLT-3 transmission, a logical “1” is transmitted by either a −1 or a +1 while a logical “0 ” is transmitted as a 0. A transmission of two consecutive logical “1”s does not require the system to pass through zero in the transition. A transmission of the logical sequence (“1”, “0”, “1”) would result in transmission of the symbols (+1, 0, −1) or (−1, 0, +1), depending on the symbols transmitted prior to this sequence. If the symbol transmitted immediately prior to the sequence was a +1, then the symbols (+1, 0, −1) are transmitted. If the symbol transmitted before this sequence was a −1, then the symbols (−1, 0, +1) are transmitted. If the symbol transmitted immediately before this sequence was a 0, then the first symbol of the sequence transmitted will be a +1 if the previous logical “1” was transmitted as a −1 and will be a −1 if the previous logical “1” was transmitted as a +1.
The detection system in the MLT-3 standard needs to distinguish between three voltage levels, instead of two voltage levels in a more typical two-level system. The signal to noise ratio required to achieve a particular bit error rate is higher for MLT-3 signaling than for two-level systems. The advantage of the MLT-3 system, however, is that the energy spectrum of the emitted radiation from the MLT-3 system is concentrated at lower frequencies and therefore more easily meets FCC radiation emission standards for transmission over twisted pair cables. Other communication systems may use a symbol alphabet having more than two voltage levels in the physical layer in order to transmit multiple bits of data using each individual symbol.
In Gigabit Ethernet over twisted pair Category-5 cabling, for example, data encoded according to the pulse amplitude modulation-5 (PAM-5) scheme can be transmitted over four twisted copper pairs at an individual twisted pair baud rate of 125 megabaud. In PAM-5, data is sent with five voltage levels, designated as symbol alphabet {A} equal to {−2, −1, 0, +1, +2}, although the values of the actual voltage levels may be different from those numbers. Each symbol, therefore, can be used to code more than one bit of data.
Any other modulation scheme for symbol coding can be utilized, including quadrature amplitude modulation (QAM). In QAM schemes, for example, the symbols are arranged on a two-dimensional (real and imaginary) symbol constellation (instead of the one-dimensional constellations of the PAM-5 and MLT-3 symbol alphabets).
There is a need for transmitters and receivers for receiving transmission over multiple twisted copper pairs using larger symbol alphabets (i.e., three or more symbols). There is also a need for transceiver (transmitter/receiver) systems that, while operating at high symbol rates, have low bit error rates.
Accordingly, a receiver and detection method for receiving transmission of data over multiple wires using encoded data symbol schemes having multiple symbols is described. A receiver according to the present invention includes multiple detectors for detecting one symbol from each of the multiple wires simultaneously (i.e., multiple one-dimensional detectors), an equalizer coupled to each of the detectors for equalizing the symbol stream from each of the multiple wires, and a multi-dimensional error analyzer/decoder for simultaneously making hard decisions regarding the symbol output of the symbols transmitted over each of the multiple wires.
Individual symbols can have any modulation scheme, including those with multi-dimensional constellations. The terminology of detecting N-dimensional (N-D) symbols refers to the number of individual symbols detected in each clock cycle, and not to the dimension of the symbol constellation.
Each of the equalizers can be any equalizer structure, including linear or decision feedback equalizers. In one embodiment of the invention, the equalizers include sequence detection equalizers. In another embodiment of the invention, the equalizers include simplified decision feedback equalizers.
In another embodiment, the equalizer includes a sequence detection equalizer in combination with a linear equalizer or a decision feedback equalizer. In some embodiments, the sequence detection equalizer is a reduced state sequence detector. In some embodiments, the decision feedback equalizer is a simplified decision feedback equalizer.
In general, a transceiver according to the present invention can utilize any symbol alphabet. In some embodiments, a PAM-5 symbol alphabet is utilized.
Some embodiments of the invention can include an error analysis decoder. The receiver receives signals from N individual wires and, for each wire, includes a linear equalizer in combination with a one-dimensional (1-D) sequence detector. The N output signals from the N 1-D sequence detectors are input to a N-D decoder that makes a final decision on the N-D symbol. In some embodiments of the invention, the error analysis decoder operates with lattice encoding schemes. In some other embodiments of the invention, the error analysis decoder operates with a parity encoding scheme.
These and other embodiments of a transceiver system according to the present invention are further described below with reference to the following figures.
In the figures, components having similar functions are often labeled similarly.
The index k in the present notation indicates the kth time cycle of the data transmission. The indicator N is an integer indicating the number of individual transport wires in cable 103. In general, any number of wires can be included in transceiver system 100. For gigabit/s transmission, N is usually 4, indicating a four wire connection between transmitter 101 and receiver system 107. Wires 103-1 through 103-4 are often twisted copper pairs.
Transmission channel 104 collectively represents cable 103 and any distortion of the signals that occurs between transmitter 101 and a receiver 107. Each of wires 103-1 through 103-N, along with output couplers of coupler 112 and input couplers of detector 108, distorts signals as indicated by the associated transmission channel 104-1 through 104-N, respectively. The signals through wires 103-1 through 103-N are distorted by channel functions f1(Z) through fN(Z), respectively, and are additionally subjected to random noise addition nk,1 through nk,N, respectively. Receiver 107 includes signal detector 108 and a decoder 109 and ultimately outputs a data stream which corresponds to the data stream entering transmitter 101.
In Gigabit Ethernet, transmission can be conducted on four twisted copper pairs (i.e., wires 103-1 through 103-4 in
Although, in general, the detection system as described here is applicable to any scheme of data transmission (i.e., any symbol alphabet) over any number of transport wires (e.g., twisted copper pairs), for exemplary purposes many of the examples below specifically describe a PAM-5 symbol alphabet transmitted over four twisted copper pairs, as would be used in Gigabit Ethernet transmission over Category-5 twisted pair cabling. It should be recognized that other symbol alphabets and numbers of conductors can also be used and that one skilled in the art will recognize from this disclosure embodiments appropriate for other modulation schemes.
Encoder
According to the developed IEEE 802.3ab standard for Gigabit Ethernet transmission, the transmitted symbols on each of four conductors 103-1 through 103-4 are chosen from a five-level pulse amplitude modulation (PAM) constellation, i.e., PAM-5, with alphabet {A} equal to {−2, −1, 0, +1, +2}. See Gigabit Standard. At each clock cycle, a single one-dimensional (1-D) symbol is transmitted on each wire. The four 1-D symbols, one on each of conductors 103-1 through 103-4, transmitted at a particular sample time k are considered to be a single 4-D symbol. In general, data entering transmitter 101 can be encoded into a N-D symbol, instead of into N 1-D symbols, by encoder 102. Encoder 102 may be any type of N-D encoder, including an N-D parity code encoder and an N-D trellis code encoder.
To achieve one gigabit/s communications, a Gigabit Ethernet transceiver needs to achieve a throughput of 250 megabits per second over each of four transport wires 103-1 through 103-4. Therefore, at a 125 megabaud rate, two bits must be transmitted at each sample time across each wire of cable 103-j of cable 103, where j is an integer running from 1 to N which is 4 here. Although a PAM-5 system is applicable, a four level PAM system, for example, does not provide redundancy which allows for error correction coding necessary to achieve a bit error rate (BER) of 10−10, as required by the Gigabit Ethernet standard. See Gigabit Standard.
In addition, extra channel symbols are needed to represent Ethernet control characters. Therefore, five-level PAM (PAM-5) with either a parity check code or trellis coding is often utilized in Gigabit Ethernet transmission. According to the Gigabit Standard, the trellis code is the only coding utilized. Alphabets having more than five-level 1-D symbols may also be utilized for gigabit/s transmission while achieving the required BER.
At 125 megabaud, each 4-D symbol needs to transmit at least eight bits. Therefore, 256 different 4-D symbols plus those required for control characters are required. By transmitting a 4-D PAM-5 symbol alphabet, there are 54=625 possible symbols. This number of symbols allows for 100% redundancy in the data as well as for several control codes. Symbol alphabets having more than five symbols yield even greater redundancy. However, because of the difficulties in distinguishing between the higher number of voltage levels, higher error rates may occur in receiver detection systems such as detector 108 of
The Gigabit Ethernet standard (see Gigabit Standard) allows a trellis code. In addition to a 4-D eight-state trellis code, a 4-D parity code has been proposed. The trellis code achieves 6 dB of coding gain over uncoded PAM-5 while the parity code achieves 3 dB of coding gain. While encoding, the choice between encoders can be encoded in a TX_CODING bit, which can be set to one for trellis coding. One skilled in the art will recognize that embodiments of the present invention are applicable to any error correction technique.
4-D Trellis Encoding
Trellis encoding in a conventional 4-D eight-state code is described in Part II, Table IV, of G. Ungerboeck, “Trellis-Coded Modulation with Redundant Signal Sets, Part I: Introduction”, IEEE Communications Mag., vol. 25, no. 2, pp. 5-11, Feb. 1987, and “Trellis-Coded Modulation with Redundant Signal Sets, Part II: State of the Art”, IEEE Communications Mag., vol. 25, no. 2, pp. 12-21, Feb. 1987 (hereinafter collectively “Ungerboeck”). An embodiment of an eight-state trellis encoder 200 similar to that described in Ungerboeck is shown in
Convolutional encoder 201 includes delays 202, 204 and 206, each of which delays its input signal by one clock cycle. The output signal from delay 202 is XORed (exclusive-ORed) with bit 6 in XOR 203 and input to delay 204. The output signal from delay 204 is XORed with bit 7 in XOR 205 and input to delay 206. The output signal from delay 206 is input to AND gate 207 and input to delay 202. AND gate 207 generates the parity bit, which is one (1) if the TX_CODING signal is 1 and the output signal from delay 206 is 1, and 0 (zero) otherwise. In embodiments that only utilize trellis coding (i.e., TX_CODING is always 1), AND gate 207 may be excluded from encoder 200 and the parity bit is the output signal from convolutional encoder 201.
The two input bits, bits 6 and 7, to convolutional encoder 201 and the parity bit produced by encoder 201 select one of eight subsets, D0 through D7, of the 4-D symbol alphabet. The nine output bits are mapped to one 4-D PAM-5 symbol which is then transmitted across cable 103 (
Each 1-D PAM-5 symbol is a member of one of two families, X (odd) and Y (even). The odd family (or type) X contains the PAM-5 symbols {−1, +1} and the even family (or type) Y contains the PAM-5 symbols {−2, 0, +2}. Table 1 shows a definition of the eight subsets D0 through D7 of the 4-D symbols. The definition is based on the membership of 1-D PAM-5 symbols that are represented in each subset Dp where subscript p is an integer varying from 0 to 7. Table 1 also shows the number of 4-D symbols in each subset Dp.
The notation describing each subset Dp indicates the families of 1-D PAM-5 symbols on each of the four wires describing membership in that subset Dp. The notation XXYX, for example, indicates a set of four 1-D PAM-5 symbols where the first symbol is from type X, the second symbol is from type X, the third symbol is from type Y, and the fourth symbol is from type X. Therefore, conductor 103-1 (
The parity bit and bits 6 and 7 are input to set select 210 (
p=4*BIT6+2*BIT7+1*Parity, (1)
where BIT6 is bit 6, BIT7 is bit 7, and Parity is the parity bit.
A point within subset Dp is chosen by the six least significant bits, bits 0 through 5, of the input. Bits 0 through 5 are input to a 4-D PAM-5 mapper 211 along with the output χ of set select 210. 4-D PAM-5 mapper 211 determines the 4-D PAM-5 symbol within subset Dp which represents the eight input bits, bits 0 through 7, and the parity bit. Each subset Dp contains more than the 64 points required to encode the six least significant bits, bits 0 through 5. These additional points are either used as control characters or not used at all.
The subset mapping shown in Table 1 is chosen such that the squared Euclidean distance between any pair of points in the same subset Dp is greater than or equal to four (4). For example, the squared distance between two points in subset D0 can be expressed as (X11−X12)**2+(X21−X22)**2+(X31−X32)**2+(X41−X42)**2 or as (Y11−Y12)**2+(Y21−Y22)**2+(Y31−Y32)**2+(Y41−Y42)**2. Because Xij=+1 or −1 and Yij=+2, 0, or −2, the shortest squared distance is (1+1)**2=(2−0)**2=4, which occurs when only one value differs between the two points. In addition, the squared Euclidean distance between points in different even-numbered subsets D0, D2, D4, and D6 is greater than or equal to 2 and the squared Euclidean distance between points in different odd-numbered subsets D1, D3, D5, and D7 is likewise greater than or equal to 2. As also can be seen from Table 1, even-numbered subsets (D0, D2, D4, and D6) have an even number of symbols of type X and an even number of symbols of type Y while odd-numbered subsets (D1, D3, D5, and D7) have an odd number of symbols of type X and an odd number of symbols of type Y.
As shown in
As a result, the minimum squared distance between valid sequences is greater than or equal to 4, which can be seen from the fact that any two paths that originate from the same node and end at the same node, but diverge at some point in the middle, must then converge at a later time. Both the divergence and the convergence have a squared distance of at least 2. The total squared distance must thus be at least 4. In the case where these two paths do not diverge, then they must contain different points from the same subset Dp. Because the minimum squared distance between points in the same subset Dp is equal to 4, the minimum squared distance between valid sequences is 4. As is conventionally known, a coding gain of 6 dB with respect to uncoded PAM-5 constellations is therefore experienced.
4-D Parity Code
The 4-D parity code can also be transmitted using the same encoder, encoder 200 of
Transmitter Coupler
Transmitter coupler 112 (
Coupler 112 converts symbols received from encoder 102 to appropriate voltages for transmission to receiver 107 through transmission channel 104. In many embodiments of PAM-5 transmission, for example, those voltages are (−1, −½, 0, +½, +1) volts corresponding to the PAM-5 symbols (−2, −1, 0, 1, 2), respectively.
Transmission Channel Characteristics
An input symbol stream {ak,1} through {ak,N} is input to each of wires 103-1 through 103-N, respectively, of transmission channel 104 (
The channel response 105-L is represented by the channel function fL(Z). In
For the sake of simplicity, a baseband transmission system is assumed, although the techniques shown are easily extended to a passband transmission system. (See E. A. L
fL(Z)=f0,L+f1,LZ−1+ . . . +fj,LZ−j+ . . . +fR,LZ−R, (2)
where f0,L, . . . , fj,L, . . . , fR,L are the polynomial coefficients, and Z−1 represents a one period delay. The coefficient fj,L represents the dispersed component of the (k−j)th symbol present in the ak,Lth symbol and R is a cut-off integer such that fj,L for j>R is negligible. The polynomial fL(Z) represents the Z-transformation of the frequency response of the transmission channel. (See A. V. O
The noiseless output vk,L of the channel at sample time k is given by
vk,L=f0,Lak,L+f1,Lak−1,L+ . . . +fR,Lak−R,L, (3)
where, without loss of generality, f0,L can be assumed to be 1. Thus, the channel output signal at time k depends, not only on transmitted data at time k, but on R past values of the transmitted data. This effect is known as “intersymbol interference” (ISI). (See L
Intersymbol interference is a result of the dispersive nature of the communication channel. The IEEE LAN standards require that systems be capable of transmitting and receiving data through at least a 100 meter cable. In many instances, a single symbol may affect symbols throughout the transmission cable.
The noise element of the input signal is represented by the sequence {nk,L}. Therefore, the noisy output signal xk,L from transmission channel 104-L is given by
xk,L=vk,L+nk,L, (4)
where the noise samples {nk,L} are assumed to be independent and identically distributed Gaussian random variables (see L
Receiver
Receiver system 500 includes receivers 501-1 through 501-N, one for each of lines 103-1 through 103-N, respectively. Receiver 501-j, an arbitrarily chosen one of receivers 501-1 through 501-N, includes filter/digitizer 502-j, equalizer 505-j, and coefficient update 506-j. Signal xk,j from wire 103-j is received by filter/digitizer 502-j. Filter/digitizer 502-j filters, digitizes and amplifies the signal xk,j and outputs a signal yk,j. Equalizer 505-j receives the signal yk,j, equalizes it to remove the effects of intersymbol interference, and outputs a signal a′k,j, which is the output signal for receiver 501-j. Filter/digitizer 502-j can be arranged to include filters that partially remove the ISI from signal xk,j before digitizing the signal. See, e.g., U.S. patent application Ser. No. 09/561,086, filed Apr. 28, 2000, Manickam et al., assigned to the same assignee as the present application, herein incorporated by reference in its entirety.
Coefficient update 506-j inputs decided-on symbols âk,j and other parameters and adaptively chooses parameters FPj and Cj respectively for filter/digitizer 502-j and equalizer 505-j (e.g., amplifier gain, multiplier coefficients, filter parameters, echo cancellation, near end crosstalk cancellation, and timing parameters).
One skilled in the art will recognize that each of receivers 501-1 through 501-N can be different. That is, each of filters/digitizers 502-1 through 502-N and equalizers 505-1 through 505-N can be individually matched to receive input signals from the corresponding one of wires 103-1 through 103-N.
Parameters to control the components of receiver 501-j can be adaptively chosen by coefficient update 506-j. Coefficient update 506-j adaptively determines the equalizer coefficients of equalizer 505-j, the gain gj of amplifier 510-j, the timing coefficient τj of ADC 509-j, and filter coefficients for filter 508-j. In some embodiments, coefficient update 506-j can calculate a baseline wander correction signal wj which is subtracted from the output sample of ADC 509-j at baseline wander correction adder 511-j. Baseline wander correction is discussed in U.S. patent application Ser. No. 09/151,525, filed Sep. 11, 1998, Raghavan, assigned to the same assignee as the present application, now U.S. Pat. No. 6,415,003, herein incorporated by reference in its entirety.
Some embodiments of receiver 501-j include a cable quality and length indicator 512-j that indicates a wire length L and wire quality Q.
Echo noise, which is a result of impedance mismatches in the duplex link causing some of the transmitted signal energy to be reflected back into a receiver, and near end crosstalk (NEXT) noise, which is caused by the interference from a transmitter, i.e., transmitter 110 (
Filter 508-j can also include an anti-aliasing filter. An anti-aliasing filter prevents aliasing by passing the input signal, received from wire 103-j, through a low pass filter to reject out-of-band noise. As such, any conventional anti-aliasing filter can be utilized as an anti-aliasing filter portion of filter 508-j.
The analog-to-digital converter (ADC) 509-j samples and holds the input signal for a duration of the symbol period T, which in one embodiment of the invention is 8 ns. In general, embodiments of the invention can utilize any symbol period. Techniques for analog-to-digital conversion that can be used in ADC 509-j are well known. The digitized signals in the receiver are interchangeably referred to in this disclosure as samples or signals.
Amplifier 510-j amplifies the samples received from wire 103-j through transmission channel 104-j in order to correct for signal loss during transmission. The gain gj of amplifier 510-j can be adaptively chosen by coefficient update 506-j in order to optimize the operation of receiver 501-j. One of ordinary skill in the art will recognize that digital amplifier 510-j can be located anywhere in receiver 501-j between ADC 509-j and equalizer 505-j. In general, amplifier 510-j can also be an analog amplifier located anywhere between input channel 104-j and ADC 509-j.
In some embodiments, coefficient update 506-j can also calculate the length and quality of wire 103-j. Cable length and quality determination is discussed in U.S. patent application Ser. No. 09/161,346, filed Sep. 25, 1998, Raghavan et al., assigned to the same assignee as the present application, now U.S. Pat. No. 6,438,163, herein incorporated by reference in its entirety.
The output sample yk,j from receiver/digitizer 502-j is input to equalizer 505-j. Equalizer 505-j can be any kind of equalizer structure. Types of equalizer structures include linear equalizers, decision feedback equalizers, and sequence detection equalizers. Equalizers of these types for 100 or 1000 BASE-T Ethernet over category-5 wiring, 24 gauge twisted copper pair, are described in U.S. patent application Ser. No. 08/974,450, filed Nov. 20, 1997, Raghavan, assigned to the same assignee as the present application, now U.S. Pat. No. 6,038,269, herein incorporated by reference in its entirety; and U.S. patent application Ser. No. 09/020,628, filed Feb. 9, 1998, Raghavan, assigned to the same assignee as the present application, now U.S. Pat. No. 6,115,418, herein incorporated by reference in its entirety.
Additionally, receivers of the type described above as receivers 501-1 through 501-N are further described in U.S. patent application Ser. Nos. 09/151,525 and 09/161,346, both cited above.
In receiver system 500 of
Equalizer 600 (
T=C0+C1Z−1+ . . . +CjZ−j+ . . . +CRZ−R. (5)
For simplicity, the wire designation L has been neglected. It is understood that each transmission channel includes a separate equalizer, which can be a unit of equalizer 600 having its own transfer function T.
In a zero-forcing linear equalizer (ZFLE), the transfer function T is the inverse of the frequency response f(Z) of the channel (see Equation 2 with the wire designation L neglected). In a minimum mean squared error based linear equalizer (MMSE-LE), the transfer function is arranged to optimize the mean squared error between the transmitted data signal and the detected data symbols. A compromise, then, is found between the un-canceled ISI and the noise variance at the output terminal of the equalizer. (See B. S
The output sample a′k from linear equalizer 600, executing transfer function T, is given by
a′k=C0yk+C1yk−1+ . . . +Cjyk−j+ . . . +CRyk−R, (6)
where C0 through CR are the equalizer coefficients, yk−j is the input signal to equalizer 600 during the time period that is j periods before the kth period, and k again represents the current time period.
The output sample a′k from equalizer 600 is usually input to a slicer 604 which decides, based on its input sample a′k, what symbol âk was transmitted during time period k. The symbol âk is chosen from the symbol alphabet used for transferring data that is closest to input signal a′k.
A linear equalizer can be implemented using either parity coding or trellis coding systems. When linear equalization is used with parity coding, a separate linear equalizer is used on each transport wire. In
As an example,
The input samples to linear equalizers 600-1 through 600-4 are the output samples yk,1 through yk,4 from receivers/digitizers 502-1 through 502-4 (
The output symbols âk,1 through âk,4 from slicers 604-1 through 604-4, respectively, are input to parity check 702. Additionally, each of samples a′k,1 through a′k,4 is subtracted from the corresponding one of symbols âk,1 through âk,4, respectively, in adders 701-1 through 701-4, respectively, to calculate errors ek,1 through ek,4, respectively. In general, the error signal ek,i, where i is 1 through 4, is then given by
ek,i=a′k,i−âk,i (7)
The parity of the 4-D symbol that results from the four 1-D symbols is checked in parity check 702. In parity coding, the 4-D symbol is chosen from an even subset of all 4-D symbols. Therefore, if PAM-5 coding is used, there are an even number of PAM-5 symbols from family X (odd symbols) and an even number from family Y (even symbols). Parity check 702 checks the parity of the four input symbols âk,1 through âk,4 by determining whether the sum of the four symbols is even or not. An odd parity indicates that there is an error in at least one of the decided-on symbols âk,1 through âk,4. The result of the parity check is input to final decoder 704.
The calculated error signals ek,1 through ek,4 are input to error analysis 703. Error analysis 703 determines which of the four error signals ek,1 through ek,4 is greatest and the sign of that error. Error analysis 703 outputs a sign signal Sgn and an identifier W for the symbol having the greatest error.
Final decoder 704 inputs the parity signal from parity check 702, the four 1-D PAM-5 symbols âk,1 through âk,4 from slicers 604-1 through 604-4, respectively, the identifier W for the symbol having the greatest error, and the sign Sgn of that error and outputs the PAM-5 symbols â′k,1 through â′k,4 in response. If the parity is even, the 4-D symbol defined by 1-D symbols â′k,1 through â′k,4 is then given by symbols âk,1 through âk,4, respectively. The parity coding scheme, therefore, can pass erroneous 4-D symbols containing simultaneous errors in two of the 1-D symbols.
If the parity is odd, however, the results of error analysis 703 are used to correct the output symbols. Because the symbol having the greatest error is the one that is most likely incorrect, the value of the symbol indicated by identifier W is corrected by either increasing or decreasing that symbol by one symbol in the symbol alphabet in response to the sign Sgn of the error (in this example, increased for a positive sign and decreased for a negative sign). The new set of four symbols, the three uncorrected symbols having the lowest error and the corrected symbol, is output as the 4-D symbol defined by 1-D symbols â′k,1 through â′k,4.
Although simple to implement, the primary disadvantage of a linear equalizer is that, while removing the ISI from the input signal, it may cause the random noise to be enhanced. This is especially true in twisted copper pair channels where the frequency response of the channel has significant attenuation across the transmitted signal bandwidth. Hence, in twisted-pair channels, such as is used with Gigabit Ethernet, linear equalization often does not perform well enough to be practical.
Adder 803 (
TFF=C0+C1Z−1+ . . . +CjZ−j+ . . . +CMZ−M. (8)
The output signal a′k,1 from feedforward section 810, therefore, is given by
a′k,1=C0yk+C1yk−1+ . . . +Cjyk−j+ . . . +CMyk−M, (9)
where yk−j is the input sample to equalizer 800 during the (k-j)th time period. Again, the wire designation has been neglected for simplicity and it is understood that each of receivers 501-1 through 501-N (
One embodiment of feedback section 811 includes delays 805-1 through 805-P coupled in series. Multipliers 806-1 through 806-P are coupled to receive the corresponding output signals from delays 805-1 through 805-P, respectively. Multipliers 806-1 through 806-P respectively multiply their input signals by the corresponding feedback multiplier coefficients B1 through Bp, respectively. Feedback coefficients B1 through Bp also can be adaptively chosen. Adder 807 sums the output signals from multipliers 806-1 through 806-P. Feedback section 811, therefore, executes the transfer function
TFB=B1Z−1+B2Z−2+ . . . +BpZ−p. (10)
The input signal to feedback section 811 is symbol âk. Consequently, the output signal a″k from feedback section 811 is given by
a″k=B1âk−1+B2âk−2+ . . . +BNâK−N. (11)
A second embodiment of feedback section 811, which is later discussed in this disclosure, is shown as feedback section 1905 in
The output signal a″k from feedback section 811 is subtracted from the output signal a′k from feedforward section 810 in adder 804. The input signal a′″k to slicer 808, then, is given by
a′″k=a″k−a′k. (12)
Slicer 808 outputs the symbol âk that is closest to the input signal a′″k.
A decision feedback equalizer operates on the principle That, if the past transmitted data is correctly detected, the ISI effects of these past data symbols can then be canceled from the currently received sample. As such, feedforward section 810 often contains no multipliers (i.e., C0=1 and all other coefficients are 0) and output sample a′k equals input sample yk.
Past detected data samples contain no noise and therefore decision feedback equalizers do not suffer from noise enhancement. However, decision feedback equalizers do suffer from the effects of error propagation. If slicer 808 erroneously determines a previous symbol, the error will be propagated into subsequent decisions.
The equalization for channel 104-1, for example, is accomplished by feedforward section (or tap) 810-1, feedback section 811-1, and adder 804-1. Similarly, channels 104-2 through 104-4, each includes the corresponding ones of feedforward sections (or taps) 810-2 through 810-4, respectively, feedback sections 811-2 through 811-4, respectively, and adders 804-2 through 804-4, respectively.
Samples yk,1 through yk,4 originate from receiver input signals received from channels 104-1 through 104-4, respectively. Samples yk,1 through yk,4 are received into feedforward taps 810-1 through 810-4, respectively. The symbol outputs â′k,1 through â′k,4 from decoder 900, corresponding to a single 4-D symbol, are input to feedback taps 811-1 through 811-4, respectively. As was discussed with relation to
In an embodiment where decoder 900 is a 4-D parity code decoder, the input signals a′″k,1 through a′″k,4 to decoder 900 are received by slicers 901-1 through 901-4, respectively. Slicers 901-1 through 901-4 respectively decide on output symbols âk,1 through âk,4 based on their corresponding input signals a′″k,1 through a′″k,4, respectively. The output symbols âk,1 through âk,4 from slicers 901-1 through 901-4 are inputted to parity check 903 and final decoder 905.
Parity check 903 sums the 1-D symbols âk,1 through âk,4 and determines whether the 4-D symbol is of even parity or odd parity. In parity coding using PAM-5 symbols, the 4-D symbol is chosen from an even subset and therefore each 4-D symbol includes an even number of 1-D PAM-5 symbols from family X (odd parity) and an even number from family Y (even parity). Therefore, the sum of the 1-D PAM-5 symbols is even. If the parity of the 4-D symbol is even, final decoder 905 outputs the symbols âk,1 through âk,4 as output symbols â′k,1 through â′k,4, respectively.
Error signals ek,1, through ek,4 are calculated in adders 902-1 through 902-4, respectively, by taking the differences between the output symbols âk,1 through âk,4 of slicers 901-1 through 901-4, respectively, and the corresponding input signals â′″k,1 through a′″k,4, respectively, for each of the transport channels:
ek,i=a′″k,i−âk,i, i=1,2,3 or 4. (13)
The error signals ek,1 through ek,4 at slicers 901-1 through 901-4, respectively, are input to error analysis 904. Error analysis 904 determines which of the symbols âk,1 through âk,4 is associated with the largest error signal ek,1, through ek,4, respectively, and the sign SGN of the largest error. Error analysis 904 outputs an identifier W of the symbol having the largest absolute error and the sign SGN of that error to final decoder 905. If the parity signal indicates odd parity, the erroneous symbol is most likely to be the one with the largest error, indicated by identifier W. Final decoder 905, then, adjusts the symbol having the largest error up or down the symbol alphabet by one symbol depending on the sign SGN (in this example, up if the sign is positive and down if the sign is negative) and outputs the resulting 4-D output symbol defined by â′k,1 through â′k,4.
The combination of N-D trellis code encoding with a DFE architecture requires a DFE on all four wires for each state within the trellis (see, e.g.,
The multiple decision feedback equalizers in the trellis decoder helps to minimize the effects of error propagation. However, a DFE architecture suffers from the disadvantage that it does not utilize the sample power contained in the intersymbol interference caused by the dispersion in the channel. More particularly, information about a 1-D symbol being transmitted during a time period k is contained in future received 1-D symbols from that channel and DFE does not utilize this signal power in determining the currently received symbol.
A third type of equalization, sequence detection, does not suffer the performance degradation of either a linear equalizer or a decision feedback equalizer. However, a typical sequence detector produces hard outputs that can severely limit the performance of an error correction code. According to the present invention, a soft-output sequence detector is provided.
As an example,
The output samples âk,1 through âk,4 from sequence detectors 1001-1 through 1001-4, respectively, along with the second best output samples â2k,1 through â2k,4, respectively, and the errors Δ1 through Δ4, respectively, are input to decoder 1002. Decoder 1002 decides on the receiver output samples â′k,1 through â′k,4 based on, for example, the parity coding scheme or the N-D lattice coding scheme. One skilled in the art will recognize that the decision of decoder 1002 can be based on any coding scheme that can correct errors in one clock cycle. Feedback is provided to sequence detectors 1001-1 through 1001-4 so that future sequences are decided using the results of the N-D decisions.
The ISI addressed by the embodiment of detector 1100 shown in
rk,w=ak,w+αw,1ak−1,w+hk,w, (14)
where αw,1 is the equalizer ISI coefficient, hk,w is the noise component of the output signal from the linear filter over a wire w and ak,w is the transmitted symbol over wire w received in time period k. Sequence detector 1100 estimates the transmitted data sequence {ak,w} from the sequence of received samples {rk,w}.
The state Sk,w, generally simply “S”, of detector 1100 is defined as the past data symbol estimates. In general, a system with a symbol alphabet having A symbols and which suffers intersymbol interference from δ previous symbols has Aδ possible states S. Each state S corresponds to a possible transition path through the δ previous symbols. For example, a system using a symbol alphabet with two symbols, {A}={+1, −1}, and subjected to ISI from two past symbols, δ=2, has four possible sequence states S of the system: symbol +1 at time k−2 and symbol +1 at time k−1; symbol +1 at time k−2 and symbol −1 at time k−1; symbol −1 at time k−2 and symbol +1 at time k−1; and symbol −1 at time k−2 and symbol −1 at time k−1. Sequence detector 1100 for the exemplary embodiment shown in
A trellis diagram depicting a state transition from time k−1 to time k for sequence detector 1100 is shown in
In sequence detector 1100 shown in
For PAM-5 signaling subjected to one ISI symbol, there are twenty-five distance metrics Mk,w(S′→S). The twenty-five distance metrics Mk,w(S′→S) generated by branch metric generator 1101 for the case where ISI is the result of one past symbol and neglecting random noise (i.e., A=5, δ=1 and fw(z)=1+αw,1z−1) are given by:
Mk,w(0)=[rk,w−(−2−2αw,1)]2; Mk,w(13)=[rk,w−αw,1)]2;
Mk,w(1)=[rk,w−(−2−αw,1)]2; Mk,w(14)=[rk,w−(2αw,1)]2;
Mk,w(2)=[rk,w−(−2)]2; Mk,w(15)=[rk,w−(1−2αw,1)]2;
Mk,w(3)=[rk,w−(−2+αw,1)]2; Mk,w(16)=[rk,w−(1−αw,1)]2;
Mk,w(4)=[rk,w−(−2+2αw,1)]2; Mk,w(17)=[rk,w−1]2;
Mk,w(5)=[rk,w−(−1−2αw,1)]2; Mk,w(18)=[rk,w−(1+αw,1)]2;
Mk,w(6)=[rk,w−(−1−αw,1)]2; Mk,w(19)=[rk,w−(1+2αw,1)]2;
Mk,w(7)=[rk,w−(−1)]2; Mk,w(20)=[rk,w−(2−2αw,1)]2;
Mk,w(8)=[rk,w−(−1+αw,1)]2; Mk,w(21)=[rk,w−(2−αw,1)]2;
Mk,w(9)=[rk,w−(−1+2αw,1)]2; Mk,w(22)=[rk,w−2]2;
Mk,w(10)=[rk,w−(−2αw,1)]2; Mk,w(23)=[rk,w−(2+αw,1)]2;
Mk,w(11)=[rk,w−(−αw,1)]2; Mk,w(24)=[rk,w−(2+2αw,1)]2;
Mk,w(12)=[rk,w]2. (15)
Each parenthetical number after “Mk,w” is a shortened notation for indicating a transition from a state S′ at time k−1 to a state S at time k.
Other metrics Mk,w(S′→S) which each represent the difference between the actual input symbol rk,w and each predicted input symbol, assuming each of the possible state transitions, may be used as distance metrics. In general, there is a distance metric Mk,w(S′→S) for every transition from any state S′ at time k−1 to state S at time k, Aδ+1 distance metrics Mk,w(S′→S) for a metrics system with A symbols and δ interfering symbols if all transitions are allowed. PAM-5 symboling is shown here only as an example and embodiments of detector 1100 can utilize other symbol alphabets and more ISI symbols.
Add-compare-select circuit 1102 in
pk,w(i)=minj={−2,−1,0,1,2}{pk−1,w(j)+Mk,w(5[i+2]+[j+2])}; (16)
where i={−2, −1, 0, 1, 2} for each possible state S and “min” means minimum.
In general, the state metrics pk,w (S) represent the accumulated distance metrics of past states along transition paths that minimize the accumulated distance metric. Therefore, the state (or transition) metric pk,w(S) for state S at time period k is the accumulated distance metric for previous states along a transition path which ends at state S at time period k, state S being one of the possible states of the system. At time k−1, the state of the system may be at any state S′ in the group of possible states of the system. Therefore, state metric pk,w (S) is the minimum one of the sum of pk−1,w(S′) and the distance metric Mk,w(S′→S) for transition from state S′ to state S. A mathematical proof that this technique results in the least detection error is given in the Appendix of U.S. patent application Ser. No. 08/974,450, cited above.
ACS circuit 1102 generates comparison results Dk,w(S), denoted by Dk,w(+2), Dk,w(+1), Dk,w(0), Dk,w(−1) and Dk,w(−2) for the PAM-5 example. In the example of
Dk,w(i)=j if pk,w(i)=pk−1,w(j)+Mk,w(5[i+2]+[j+2]), (17)
where i={−2, −1, 0, 1, 2} for each possible state S and j={−2, −1, 0, 1, 2}. In general, each comparison result Dk,w(S) points toward the state S′ at time k−1 from which results the lowest state metric pk,w(S) for arriving at state S at time k.
When it is time for decoding, traceback circuit 1103 traces back from a starting state, and fetches the data from memory in traceback circuit 1103.
In one example of a traceback, if the traceback depth is 2*TB, then it is expected that a traceback of TB is performed every TB/2 sample times and traceback circuit 1103 outputs TB/2 data symbols. With little loss of generality, TB can be an even integer such as 6, 8 or 16. A greater traceback depth will result in less error in determining the final sequence of symbols. Greater traceback depths, however, incur an implementation cost of requiring more memory in traceback circuit 1103.
During the traceback procedure, starting state determiner 1105 picks the starting state, which can be based on the state metrics pk,w (S). Traceback circuit 1103 follows the sequence back through the comparison results Dk,w(S) stored in memory in traceback circuit 1103. The earliest TB/2 symbols, which result in the earliest states, are written into last-in-first-out buffer 1104. The new comparison results Dk,w(S) are stored in the memory locations previously occupied by the outputted comparison results Dk,w (S).
Traceback circuit 1103 determines the optimum sequence of symbols âk,w based on the state metrics pk,w(S) stored in starting state determiner 1105. Starting state determiner 1105 initializes the traceback procedure by setting a starting sequence.
LIFO 1104 simply time-reverses the data âk,w coming out of traceback circuit 1103 because the traceback is performed from the current time to previous times.
Sequence Detection with Pre-Equalization
When the channel ISI length δ is large, or if the transmitted symbol alphabet size A is large, the above method of full sequence estimation becomes impractical at high symbol rates. Full sequence estimations require the implementation of Aδ states in the detector. Accordingly, an equalizer 1110 is employed with sequence detector 1100 to provide pre-equalization by preprocessing the input samples yk,w in order to reduce the number of ISI symbols to be processed by sequence detector 1100. Equalizer 1110 can be any equalizer that reduces the number of ISI symbols. For purposes of example, assume that the channel input alphabet size A is 5, i.e., {A}={+2, +1, 0, −1, −2}, and that the reduced ISI length δ′, as seen by sequence detector 1100, is 1. As before, the technique is applicable to larger alphabets and may accommodate more than one interfering symbol in the reduced length.
Repeating Equation 14, the output rk,w of the equalizer 1110 with A=5 and δ′=1 is given by
rk,w=ak,w+αw,1ak−1,w+hk,w, (18)
where αw,1 is again the equalized ISI coefficient and hk,w is again the noise component of the output of the linear equalizer 1110. The transfer function Ew(z) (in z-transform notation, see A. V. O
Ew(z)=(1+αw,1z−1)/fw(z). (19)
The coefficient αw,1 is chosen to minimize the noise variance at the equalizer output. Equalizer 1110, therefore, is a reduced sequence equalizer because it reduces the ISI length from δ to δ′. The reduced ISI length δ′ is 1 in this example.
In one embodiment, reduced sequence equalizer 1110 is implemented adaptively. One architecture used for adaptive implementation is shown in
The coefficients αw,1 through αw,δ′ can be chosen adaptively in sequence detector 1100 by observing the frequency response of linear equalizer 1120. From linear equalizer 1120, the channel frequency response is deduced and coefficients αw,1 through αw,δ′ can be selected from a look-up table. In one embodiment with reduced ISI length δ′ equal to 1, two possible values (0 and ½) of coefficient αw,1 are used. One of the two possible values is chosen by observing the two largest equalizer coefficients C0 and C1 of linear equalizer 1120. For example, in one embodiment, coefficient αw,1 is 0.5 if C1/C0 is less than −0.5. Otherwise, coefficient αw,1 is 0.
The benefits of combining linear equalization with sequence detection include (a) reduced complexity in the sequence detector, especially for large ISI lengths, and (b) reduced noise enhancement in the linear equalization.
In the example described above in connection with
Sequence Detection with Pre-Equalization and Decision Feedback
Gw(z)=1+αw,1z−1+αw,2z−2. (20)
The transfer function Ew(z) of equalizer 1301 is given by
Ew(z)=Gw(z)/fw(z). (21)
Sequence detector 1300 includes branch metric generator 1302, add compare select (unit) 1303, traceback (circuit) 1304, LIFO 1305 and starting point determiner 1306. In general, the detection technique implemented in sequence estimator 1300 may be used for any combination of transmission-channel ISI length δ and pre-equalized ISI polynomial length η such that η≦δ. Although the technique may be implemented with any sized alphabet, the example shown in
To perform the sequence estimation using the Viterbi algorithm, as outlined above, sequence detector 1300 is still implemented with twenty-five states (if the data symbols are PAM-5 values). The branch metric computations from a trellis diagram now account for the intersymbol interference due to the symbols transmitted two sample times before as well as the symbol transmitted during the last period. In one embodiment, the branch metrics Mk,w(S′→S) computed by branch metric generator 1302 with decision feedback are given by:
Mk,w(0)=[rk,w−αw,2Dk−1(−2)−(−2−2αw,1)]2;
Mk,w(1)=[rk,w−αw,2Dk−1(−1)−(−2−αw,1)]2;
Mk,w(2)=[rk,w−αw,2Dk−1(0)−(−2)]2;
Mk,w(3)=[rk,w−αw,2Dk−1(1)−(−2+αw,1)]2;
Mk,w(4)=[rk,w−αw,2Dk−1(2)−(−2+2αw,1)]2;
Mk,w(5)=[rk,w−αw,2Dk−1(−2)−(−1−2αw,1)]2;
Mk,w(6)=[rk,w−αw,2Dk−1(−1)−(−1−αw,1)]2;
Mk,w(7)=[rk,w−αw,2Dk−1(0)−(−1)]2;
Mk,w(8)=[rk,w−αw,2Dk−1(1)−(−1+αw,1)]2;
Mk,w(9)=[rk,w−αw,2Dk−1(2)−(−1+2αw,1)]2;
Mk,w(10)=[rk,w−αw,2Dk−1(−2)−(−2αw,1)]2;
Mk,w(11)=[rk,w−αw,2Dk−1(−1)−(−αw,1)]2;
Mk,w(12)=[rk,w−αw,2Dk−1(0)]2;
Mk,w(13)=[rk,w−αw,2Dk−1(1)−αw,1]2;
Mk,w(14)=[rk,w−αw,2Dk−1(2)−2αw,1]2;
Mk,w(15)=[rk,w−αw,2Dk−1(−2)−(1−2αw,1)]2;
Mk,w(16)=[rk,w−αw,2Dk−1(−1)−(1−αw,1)]2;
Mk,w(17)=[rk,w−αw,2Dk−1(0)−1]2;
Mk,w(18)=[rk,w−αw,2Dk−1(1)−(1+αw,1)]2;
Mk,w(19)=[rk,w−αw,2Dk−1(2)−(1+2αw,1)]2;
Mk,w(20)=[rk,w−αw,2Dk−1(−2)−(2−2αw,1)]2;
Mk,w(21)=[rk,w−αw,2Dk−1(−1)−(2−αw,1)]2;
Mk,w(22)=[rk,w−αw,2Dk−1(0)−2]2;
Mk,w(23)=[rk,w−αw,2Dk−1(1)−(2+αw,1)]2;
Mk,w(24)=[rk,w−αw,2Dk−1(2)−(2+2αw,1)]2. (22)
The ISI due to the transmitted symbol at time k−2 is removed from the received sample rk,w before the branch metric Mk,w(S′→S) that accounts for the ISI due to the transmitted symbol at time k−1 is computed. After this calculation, the previously described calculation is performed to remove the ISI due to the (k−1)th transmitted symbol.
Add compare select 1303 then computes the state metrics pk,w(i) and the comparison results Dk,w(i) as described above in Equations 16 and 17, respectively. Traceback 1304 accepts a starting point from starting point determiner 1306, as described above for the corresponding components of sequence detector 1100 in
Sequence Detection in Combination with Error Correction
Although achieving excellent noise margins, the combination of sequence detection with error correction codes is problematic. Sequence detectors usually produce hard decisions (i.e., decisions that do not contain information on reliability), which become input signals to error correcting codes. Most error correcting techniques, such as the parity coding or 4-D lattice coding proposed for Gigabit Ethernet, rely on soft decisions (i.e., decisions that contain reliability information) to achieve full performance. See, e.g., S. L
Traceback 1404 is coupled to each wire w so that the traceback can be accomplished on N-D symbols rather than performing a separate traceback on N 1-D symbols, where N is the number of wires. Traceback 1404 is also coupled with LIFO 1405. LIFO 1405 outputs the final symbol stream {â′k,w} for each wire w.
A sequence detector according to the present invention can accommodate any symbol alphabet {A} and any number δ of ISI symbols. For example, sequence detector 1400-w shown in
Add compare select 1403-w computes the state metrics pk,w(i) for i={−2, −1, 0, 1, 2} according to Equation 16 and the ACS results Dk,w(i) for i={−2, −1, 0, 1, 2} according to Equation 17. Additionally, ACS 1403-w computes a second best state metric p2k,w(i), a second ACS result D2k,w(i), and a difference result Δk,w(i). The second best state metric p2k,w(i) can be computed according to
p2k,w(i)=second minj={−2,−1,0,1,2}{pk−1,w(i)+Mk,w(5[i+2]+[j+2])}, (23)
where i={−2, −1, 0, 1, 2} and “min” again means minimum. The second ACS result D2k,w(i) can be computed according to
D2k,w(i)=j if p2k,w(i)=pk−1,w(j)+Mk,w(5[i+2]+[j+2]), (24)
where i={−2, −1, 0, 1, 2} and j={−2, −1, 0, 1, 2}. Finally, the difference result Δk,w(i) can be computed according to
Δk,w(i)=p2k,w(i)−pk,w(i), (25)
where again i={−2, −1, 0, 1, 2}. Traceback 1404 receives the best ACS results Dk,w(i), the second best ACS results D2k,w(i), and the difference results Δk,w (i) from each state on each wire was well as a starting point signal Sw from starting point determiner 1406-w for each wire w.
Traceback 1404 includes four read modules 1501-1 through 1501-4, one for each of the four wires. Each read module 1501-1 through 1501-4 receives parameters Γk,w from add compare select 1403-w and starting point determiner 1406-w (
Traceback 1404 in
As described above, the 4-D parity coding scheme only transmits 4-D symbols having even parity. A single error in one 1-D symbol will cause the parity of the 4-D symbol to become odd. Similar to “4-D slicing”, traceback 1404 recognizes the parity error and makes corrections to the four 1-D symbols from read modules 1501-1 through 1501-4 for clock cycle k based on the reliability of each of the 1-D symbols.
Hagenauer has shown that, within a Viterbi decoder, the reliability of decision symbol paths merging at each state grows with the difference between the state metrics between the two paths. See J. Hagenauer and P. Hocher, “A Viterbi Algorithm with Soft-Decision Outputs and its Applications,” Proc. GLOBECOM '89, pages 1680-1686, November 1989. Similar to Hagenauer's Soft Output Viterbi Algorithm (SOVA), each of read modules 1501-1 through 1501-4 outputs the difference metric εk,1 through εk,4, respectively, i.e., the reliability measure, between the best two paths entering each state. SOVA uses difference metrics εk,1 through εk,4 over a range of sample times within the trellis to output soft decisions for every symbol.
However, 4-D parity traceback 1404 can recognize when a single error occurs. Therefore, only the difference metrics εk,1 through εk,4 at the time of the error are required to correct errors. Because the actual decoding is accomplished during traceback in each of sequence detectors 1400-1 through 1400-4, traceback 1404 recognizes an error in its channel and corrects the error in its own sequence path.
For each clock cycle k, traceback 1404 retrieves the first choice 1-D symbols âk,1 through âk,4, the second choice 1-D symbols â2k,1 through â2k,4, and the reliability measures εk,1 through εk,4, and determines the finally decided-on four 1-D symbols â′k,1 through â′k,4.
For each clock cycle k, parity check 1502 receives the first choice symbols âk,1 through âk,4 from read modules 1501-1 through 1501-4, respectively, determines the parity of the resulting 4-D symbol and outputs a parity signal indicating the parity of the 4-D symbol. Error analysis 1503 receives reliability measures εk,1, through εk,4 from read modules 1501-1 through 1501-4, respectively, determines which of the sequence detectors 1400-1 through 1400-4 has the least reliability, thereby indicating which result is most likely to be incorrect, and outputs a wire signal W indicating which of first choice 1-D symbols âk,1, through âk,4 is most likely to be incorrect. Decoder 1504 receives the first choice symbols âk,1 through âk,4, the second choice symbols â2k,1 through â2k,4, the parity signal from parity check 1502, and the wire signal W from error analysis 1503.
If the parity signal indicates that the parity of the first choice 4-D symbol is even, then the first choice symbols âk,1 through âk,4 are output as the finally decided-on symbols â′k,1 through â′k,4. However, an odd parity indicates an error in one of the first choice symbols âk,1 through âk,4. If the parity signal indicates an odd parity, the symbol indicated by the wire signal W is replaced by a corresponding one of second choice symbols â2k,1 through â2k,4 and the resulting 4-D symbol is output as finally decided-on symbols â′k,1 through â′k,4.
Additionally, decoder 1504 informs read modules 1501-1 through 1501-4 of the finally decided-on symbols â′k,1 through â′k,4 by indicating, for each of read modules 1501-1 through 1501-4, which of the first choice symbols âk,1 through âk,4 or the second choice symbols â2k,1 through â2k,4 was output as the finally decided-on symbols â′k,1 through â′k,4 for clock cycle k. Read modules 1501-1 through 1501-4 can then traceback accordingly and respectively output the first choice symbols âk−1,1 through âk−1,4, the second choice symbols â2k−1,1 through â2k−1,4, and the reliability measures εk−1,1 through εk−1,4 for clock cycle k−1.
In other words, read module 1501-w outputs the best possible step back âk,w, the second best step back â2k,w, and the reliability measure εk,w for each wire w for clock cycle k. Parity check 1502 performs a parity check on the best possible step back âk,w. Error analysis 1503 determines the wire w most likely to be incorrect. If the parity passes, decoder 1504 outputs the best possible step back âk,w for clock cycle k. If parity fails, then decoder 1504 replaces one of the best possible symbols âk,w with the associated second best symbol â2k,w, based on which wire w is most likely to be incorrect, and outputs the resulting 4-D symbol. The choice of best symbol âk,w or second best symbol â2k,w for each wire w is communicated back to read module 1501-w so that read module 1501-w can use the appropriate symbol âk,w or â2k,w to step back to clock cycle k−1. The replacement choice then affects only one read module 1501-w. Therefore, the next set of symbols will be affected in one read module 1501-w only.
As shown in
One skilled in the art will recognize that in general a sequence detector according to this invention can accommodate any symbol alphabet and the effects of any number of ISI symbols. Additionally, the sequence detector may include decision feedback as shown in
Reduced Complexity Sequence Detection Using State Reduction
If the alphabet size is large or if the ISI length at the sequence detector is large, sequence detector 1400-w shown in
As mentioned above, the PAM-5 symbol alphabet can be segregated into two families, an odd family X having the PAM-5 symbols {−1, +1} and an even family Y having the PAM-5 symbols {−2, 0, +2}. A detector state can now be defined as the previous η families X and Y, as opposed to the previous η PAM-5 symbols {−2, −1, 0, +1, +2}. Therefore, the number of states required for the PAM-5 symbol alphabet with η=2 ISI symbols is reduced from 25 states to 4 states on each transmission channel w=1 through L. For a four wire system (4-D decoding, for example), there are a total of sixteen states instead of one hundred states.
Reduced state detection can be accomplished when the minimum squared distance between any two parallel branches of a state transition S→S′ exceeds the minimum squared distance between any two paths in the trellis where the definitions of states S and S′ are reversed from that used earlier. A parallel branch refers to transitions S→S′ between individual states through different symbols. For example, a state S=X can transition to a state S′=X through receipt of either a −1 symbol or a +1 symbol.
The actual minimum squared distance between sequences does not decrease and thus the performance undergoes little or no degradation from that of full state sequence detection. Gigabit Ethernet using a PAM-5 symbol set subjected to ISI from two symbols meets this criteria.
In
E(Z)=(1+α1Z−1+α2Z−2)/f(Z). (26)
Therefore, the expected signal input rk,w to decoder system 1600 is
rk,w=ak,w+α1ak−1,w+α2ak−2,w. (27)
Branch metric generator 1602-w computes the branch metrics Mk,w(S→S′) for the state transitions displayed in FIG. 17. In the reduced state trellis shown in
For each state S at k−1, symbols âk−1(S) and âk−2(S) are known based upon feedback from ACS 1603-w to branch metric generator 1602-w as shown in
σ(S→S′)=rk,wα1âk−1,w(S)−α2âk−2,w(S). (28)
The difference σ(S→S′) is then compared with the symbols for each possible branch of the state transition S to S′. The symbol chosen a′k,w(S→S′) for the branch is then assigned to the transition from state S to state S.
With reference to
Mk,w(S→S′)=[rk,w−a′k,w(S→S′)−α1âk−1,w(S)−α2âk−2,w(S)]2, (29)
where the valid transitions (S→S′) in
Add-compare-select 1603-w receives the branch metrics Mk,w(S→S′) and branch decisions Bk,w(S→S′) from branch metric generator 1602-w and calculates the state metrics pk,w(S′) according to the equation
pk,w(S′)=minj={S}{pk−1,w(j)+Mk,w(S→S′)}, (30)
where j is equal to each S such that S→S′ is allowable and “min” once again means minimum.
Add-compare-select 1603-w also determines the ACS comparison result Dk,w(S′) and the ACS error result Δk,w(S′) for each of the four final states S′ and communicates those results Dk,w(S′) and Δk,w(S′) to traceback circuit 1604. The ACS comparison result Dk,w(S′) is the path resulting in state S′ having the lowest branch metric Mk,w(S→S′). Because there are only two allowed paths that result in state S′ (see
The error Δk,w(S′) is the difference in branch metrics Mk,w(S→S′) between the two paths resulting in state S′:
Δk,w(S′)=|Mk,w(S1→S′)−Mk,w(S2−S′)| (31)
where S1 is one of the two initial states that transition to the final state S′ and S2 is the other of the two initial states that transition to the final state S′. For example, from
Finally, the branch decisions Bk,w(S→S′) of branch metric generator 1602-w are also communicated from add-compare select 1603-w to traceback circuit 1604 in the form of ACS branch decisions B1k,w(S′) and B2k,w(S′). Branch decision B1k,w(S′) corresponds to the decision on the path S→S′ indicated by Dk,w(S′). Branch decision B2k,w(S′) corresponds to the decision on the path S→S′ contraindicated by Dk,w(S′). Therefore, in the soft-decision process, if the traceback circuit 1604 is altered to the second most likely path, the parallel path decision for the second most likely path is available to traceback circuit 1604.
Traceback circuit 1604 can be the same as traceback 1404 of
As is shown in
In sequence detector 1600-w of
As was previously discussed, the 4-D parity code provides 3 dB of coding gain, which doubles the minimum squared distance between possible paths. However, this code provides no protection between parallel branches of transitions along one wire. Therefore, this overall requirement on minimum distances prevents the minimum squared distance from decreasing because of reduced state detection. This requirement holds for Gigabit Ethernet standards, as described above. Although the requirement should hold in general, it may not be held for all embodiments of the invention.
Simplified Decision Feedback Equalization
Reduced sequence detection can also be accomplished utilizing decision feedback equalization (DFE). However, a simplified DFE provides a simple and easy implementation for accomplishing the equalization process in the allotted time (8 ns in the example of gigabit/s transmission over four wires).
shows an example of a simplified decision feedback equalizer 1900. The simplified decision feedback equalizer 1900 includes a pre-equalizer section 1901, an adder 1902, a slicer 1903, and a feedback section 1905. Pre-equalizer section 1901 can be any equalizer structure that reduces the ISI length to L symbols. Pre-equalizer section 1901, therefore, executes the transfer function
T(Z)=(1+α1Z−1+ . . . +αLZ−L)/f(Z) (32)
where α1 through αL are the multiplier coefficients of pre-equalizer section 1901 and f(Z) is the response of the input channel (see Equation 2 for the response of a transfer channel).
The output signal a′k from pre-equalizer (or feedforward) section 1901 is input to adder 1902. Adder 1902 subtracts the signal a″k provided by selector 1906 from the output signal a′k provided by feedforward section 1901. The resulting signal a′″k=a′k−a″k is input to slicer 1903. Slicer 1903 outputs a symbol âk that is closest to the input signal a′″k. The feedback section 1905 (see also feedback section 811 of
In some embodiments, selector 1906 receives the look-up values ξ1 through ξQ as input signals. In some embodiments, the look-up values ξ1 through ξQ are preset. The look-up values ξ1 through ξQ can also be adaptively chosen to optimize performance of the receiver of which decision feedback equalizer 1900 is a part. In most embodiments, Q=AL where A is the size of the symbol alphabet.
As an example, in a system using the PAM-5 alphabet where L is 2 and Q is 25, there are twenty-five look-up values ξ1 through ξ25. Because the intersymbol interference in the input signal to adder 1902 is the result of two ISI symbols,
a′k=ak+αak−1+βak−2+nk, (33)
where α and β are the interference parameters and nk is random noise. The twenty-five values ξ1 through ξ25 for the look-up table, therefore, are given by:
a″k=ξ1=2α+2β if (âk−1=2) and (âk−2=2);
a″k=ξ2=2α+β if (âk−1=2) and (âk−2=1);
a″k=ξ3=2α if (âk−1=2) and (âk−2=0);
a″k=ξ4=2α−β if (âk−1=2) and (âk−2=−1);
a″k=ξ5=2α−2β if (âk−1=2) and (âk−2=−2);
a″k=ξ6=α+2β if (âk−1=1) and (âk−2=2);
a″k=ξ7=α+β if (âk−1=1) and (âk−2=1);
a″k=ξ8=α if (âk−1=1) and (âk−2=0);
a″k=ξ9=α−β if (âk−1=1) and (âk−2=−1);
a″k=ξ10=α−2β if (âk−1=1) and (âk−2=−2);
a″k=ξ11=2β if (âk−1=0) and (âk−2=2);
a″k=ξ12=β if (âk−1=0) and (âk−2=1);
a″k=ξ13=0 if (âk−1=0) and (âk−2=0);
a″k=ξ14=−β if (âk−1=0) and (âk−2=−1);
a″k=ξ15=−2β if (âk−1=0) and (âk−2=−2);
a″k=ξ16=−α+2β if (âk−1=−1) and (âk−2=2);
a″k=ξ17=−α+β if (âk−1=−1) and (âk−2=1);
a″k=ξ18=−α if (âk−1=−1) and (âk−2=0);
a″k=ξ19=−α−β if (âk−1=−1) and (âk−2=−1);
a″k=ξ20=−α−2β if (âk−1=−1) and (âk−2=−2);
a″k=ξ21=−2α+2β if (âk−1=−2) and (âk−2=2);
a″k=ξ22=−2α+β if (âk−1=−2) and (âk−2=1);
a″k=ξ23=−2α if (âk−1=−2) and (âk−2=0);
a″k=ξ24=−2α−β if (âk−1=−2) and (âk−2=−1);
a″k=ξ25=−2α−2β if (âk−1=−2) and (âk−2=−2). (34)
The parameters α and β can be adaptively chosen and the table updated periodically by calculating the look-up values ξ1 through ξQ and inputting them into selector 1906. When decision feedback equalizer 1900 is utilized, for example, as equalizer 505-j in receiver 501-j of
Pre-equalizer section 2001 of sequence detector 2000 receives signal yk,w, and executes a transfer function, such as that of Equation 32, which removes the ISI influence of all but L past symbols. Feedback section 2003 outputs a signal a″k that removes the influence of an additional M past symbols based on the inputs from add-compare-select (unit) 2005. Sequence detector 2000 therefore utilizes states describing the past L-M ISI symbols.
As occurs in branch metric generators 1101, 1302, 1402-w, and 1602-w, branch metric generator 2004 outputs a set of branch metrics Mk,w(S→S′) for transitions between states S and state S′ of the decoder. ACS 2005 outputs the ACS results Dk,w(S′) to traceback circuitry 2006, and the state (or transition) metrics pk,w(S′) to starting point determiner 2007. Traceback circuit 2006 outputs the symbols decided by sequence detector 2000 in reverse chronological order, and LIFO 2008 reverses the order of those symbols to output symbol stream {âk,w}.
The output signals Sk,w outputted from ACS 2005 to feedback section 2003 are given by the traced back sequence from traceback circuit 2006.
From
One embodiment of feedback section 2003 includes feedback sections like feedback section 811. For Gigabit Ethernet, at symbol rates of 125 Mhz on each wire, the timing constraints of the sequence detector are severe. When “per-survivor processing” (see, e.g., sequence detector 1300 of
The embodiments discussed above are exemplary only and are not intended to be limiting. One skilled in the art will recognize multiple variations of these embodiments that are intended to be included within the scope of this disclosure. As such, the invention is limited only by the following claims.
This is a continuation of U.S. patent application Ser. No. 11/044,537, filed Jan. 27, 2005, now abandoned, which is a division of U.S. patent application Ser. No. 09/560,109, filed Apr. 28, 2000, now U.S. Pat. No. 7,050,517 B1.
| Number | Name | Date | Kind |
|---|---|---|---|
| 5291499 | Behrens et al. | Mar 1994 | A |
| 5502735 | Cooper | Mar 1996 | A |
| 5602507 | Suzuki | Feb 1997 | A |
| 5638065 | Hassner et al. | Jun 1997 | A |
| 5654667 | Adachi | Aug 1997 | A |
| 5809079 | Hayashi | Sep 1998 | A |
| 5841478 | Hu et al. | Nov 1998 | A |
| 5859861 | Oh | Jan 1999 | A |
| 5960011 | Oh | Sep 1999 | A |
| 6035007 | Khayrallah et al. | Mar 2000 | A |
| 6038269 | Raghavan | Mar 2000 | A |
| 6041433 | Kamada | Mar 2000 | A |
| 6047024 | How | Apr 2000 | A |
| 6215744 | Mita et al. | Apr 2001 | B1 |
| 6226332 | Agazzi et al. | May 2001 | B1 |
| 6252904 | Agazzi et al. | Jun 2001 | B1 |
| 6253345 | Agazzi et al. | Jun 2001 | B1 |
| 6256352 | Chang | Jul 2001 | B1 |
| 6289063 | Duxbury | Sep 2001 | B1 |
| 6356586 | Krishnamoorthy et al. | Mar 2002 | B1 |
| 6408420 | Todoroki | Jun 2002 | B1 |
| 6418172 | Raghavan et al. | Jul 2002 | B1 |
| Number | Date | Country |
|---|---|---|
| 19626076 | Jan 1997 | DE |
| 02-215236 | Aug 1990 | JP |
| 06-334692 | Dec 1994 | JP |
| 08-116275 | May 1996 | JP |
| 08-172366 | Jul 1996 | JP |
| 09-148944 | Jun 1997 | JP |
| WO9711544 | Mar 1997 | WO |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 09560109 | Apr 2000 | US |
| Child | 11044537 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 11044537 | Jan 2005 | US |
| Child | 11517435 | US |
