Vector signaling codes with high pin-efficiency for chip-to-chip communication and storage

Abstract

An alternative type of vector signaling codes having increased pin-efficiency normal vector signaling codes is described. Receivers for these Permutation Modulation codes of Type II use comparators requiring at most one fixed reference voltage. The resulting systems can allow for a better immunity to ISI-noise than those using conventional multilevel signaling such as PAM-X. These codes are also particularly advantageous for storage and recovery of information in memory, as in a DRAM.

Description

BACKGROUND OF THE INVENTION

The present invention relates to communications in general and in particular to the transmission of signals capable of conveying information and detection of those signals in chip-to-chip communication.

In communication systems, a goal is to transport information from one physical location to another. It is typically desirable that the transport of this information is reliable, is fast and consumes a minimal amount of resources. One common information transfer medium is the serial communications link, which may be based on a single wire circuit relative to ground or other common reference, or multiple such circuits relative to ground or other common reference. A common example uses singled-ended signaling (“SES”). SES operates by sending a signal on one wire, and measuring the signal relative to a fixed reference at the receiver. A serial communication link may also be based on multiple circuits used in relation to each other. A common example of the latter uses differential signaling (“DS”). Differential signaling operates by sending a signal on one wire and the opposite of that signal on a matching wire. The signal information is represented by the difference between the wires, rather than their absolute values relative to ground or other fixed reference.

There are a number of signaling methods that maintain the desirable properties of DS while increasing pin efficiency over DS. Vector signaling is a method of signaling. With vector signaling, a plurality of signals on a plurality of wires is considered collectively although each of the plurality of signals might be independent. Each of the collective signals is referred to as a component and the number of plurality of wires is referred to as the “dimension” of the vector. In some embodiments, the signal on one wire is entirely dependent on the signal on another wire, as is the case with DS pairs, so in some cases the dimension of the vector might refer to the number of degrees of freedom of signals on the plurality of wires instead of exactly the number of wires in the plurality of wires.

With binary vector signaling, each component or “symbol” of the vector takes on one of two possible values. With non-binary vector signaling, each symbol has a value that is a selection from a set of more than two possible values. Any suitable subset of a vector signaling code denotes a “sub code” of that code. Such a subcode may itself be a vector signaling code.

A vector signaling code, as described herein, is a collection C of vectors of the same length N, called codewords, a second collection A of vectors of length N+1, called multi-input comparators (MIC's) comparing a linear combination of the values on the wires against another linear combination, and a set of “Inactive” elements wherein each inactive is a pair (c, λ), c being an element of C, and λ being an element of Λ. A pair (c, λ) that is not inactive is called “active.” In operation, the coordinates of the codewords are bounded, and we choose to represent them by real numbers between −1 and 1. The ratio between the binary logarithm of the size of C and the length N is called the pin-efficiency of the vector signaling code.

In operation, a MIC represented by a vector (ml, . . . , mN, mN+1) calculates the sign of the scalar product of the vector (ml, . . . , mN) with the vector of the N values on the wires, compares the outcome against the value mN+1, also called the reference of the MIC, and outputs a binary value corresponding to the computed sign. A MIC with reference 0 is called “central.” A central MIC with the property that the sum of its coordinates is 0 as well is called “common mode resistant.” This is because the operation of this MIC is independent of changing the values of all the wires by the same “common mode” value. If all MIC's are central, then we remove the final coordinate (i.e., the reference) of the MIC, and represent the MIC by its N first coordinates only.

In operation, a codeword is uniquely determined by the vector of signs of scalar products of that codeword c with all the MIC's λ, for which (c, λ) is active.

A vector signaling code is called “balanced” if for all its codewords the sum of the coordinates is always zero. Balanced vector signaling codes have several important properties. For example, as is well-known to those of skill in the art, balanced codewords lead to lower electromagnetic interference (EMI) noise than non-balanced ones. Also, if common mode resistant communication is required, it is advisable to use balanced codewords, since otherwise power is spent on generating a common mode component that is cancelled at the receiver.

Another fundamental parameter of a vector signaling code is its ISI ratio as defined in Hormati I: the ISI ratio of a MIC λ for the given set C of codewords is the ratio of the largest scalar product |<λ,c>| to the smallest scalar product |<λ,d>| for all codewords c and d such that (c, λ) and (d, λ) are active. A code is said to have ISI ratio x if x is the maximum of the ISI ratios of its MIC's. As taught by Hormati I, the lower the ISI ratio, the less susceptible the vector signaling code is to intersymbol interference noise.

For example, DS is a vector signaling code of length 2, and pin-efficiency ½ consisting of the codewords (1,−1) and (−1,1). The set Λ of MIC's contains one MIC only, given by the vector (1,−1). DS is balanced and has ISI ratio 1.

A class of vector signaling codes disclosed in Cronie II is the class of permutation modulation or PM codes of Slepian, first described in Slepian I for other communication settings. These codes have the property that each codeword is a permutation of a vector x₀. The vector x₀ is called the generator of the signal constellation and the signal constellation defines a permutation modulation code. In a preferred embodiment the vector x₀ is defined by a sequence of m integersl₀≦l₁≦□≦l_m-1  (Eqn. 1)

It follows that

$N=\sum _{i=0}^{m-1}{l}_i.$ The generator x₀ may have the form

$\begin{array}{cc}{x}_0=\left(\underset{l_0}{\underbrace{a_0,\dots ,a_0}}|\underset{l_1}{\underbrace{a_1,\dots ,a_1}}\dots \underset{l_{m-1}}{\underbrace{a_{m-1},\dots ,a_{m-1}}}\right)& \left(\mathrm{Eqn}.2\right)\end{array}$ where a₀ to a_m-1 are non-zero numbers such that

$\sum _{i=0}^{m-1}{l}_i{a}_i=0.$

PM-codes have a number of important and practically relevant properties. For example, they can be detected using common-mode resistant comparators. In very high speed applications, and where there is expectation that a reference value may be subject to change depending on the communications conditions, reference-less comparators often lead to a higher signal margin and hence to a higher integrity of the recovered signals. Moreover, since the net current sum on all the interface wires is zero, this type of vector signaling code produces less EMI noise than otherwise; in addition, since no energy is launched into the common mode of the wires, this type of signaling is also efficient in terms of the power it uses.

An example of a typical systems environment incorporating vector signaling code communication is shown in FIG. 1.

Information to be transmitted 100 is obtained from a source SRC and presented to transmitter 120. Within the transmitter, the information is encoded 122 as symbols of a vector signaling code 125, which are then presented to transmit driver 128, generating physical representations of the code symbols on a collection of wires 145 which together comprise the communications channel 140.

Receiver 160 accepts physical signals from communications channel 140, detects the received codewords using, as one example, a collection of differential binary MIC's 166, and then decodes 168 those detected values 167 to obtain the received information 180 output to a destination device DST.

In a practical embodiment, signals 145 may undergo significant change in amplitude, waveform, and other characteristics between emission by transmitter 120 and arrival at receiver 160, due to the transmission characteristics of communications channel 140. Therefore, it is common practice to incorporate signal amplification and/or equalization 162 into communications channel receivers.

Examples of vector signaling methods are described in Cronie I, Cronie II, Cronie III, Fox I, Fox II, Fox III, Holden I, Shokrollahi I, Shokrollahi II, and Hormati I. For these vector signaling codes, the comparators 166 are all common mode resistant, i.e., they compare a linear combination of some of the values against a linear combination of some other values, and the sum of the weights of each of these linear combinations is the same.

BRIEF SUMMARY OF THE INVENTION

An alternative type of vector signaling codes is described which have a larger pin-efficiency than normal vector signaling codes, may be received using comparators requiring at most one fixed reference voltage, and which can allow for a better immunity to ISI-noise than conventional multilevel signaling such as PAM-X. This alternative type of vector signaling codes are also particularly applicable to applications requiring the efficient and reliable storage of information, one example being Dynamic memory devices.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a typical prior art vector signaling code system.

FIG. 2 is a schematic of an embodiment of a receive codeword detector in accordance with at least one aspect of the present invention, acting as a detector of a PM-II code on 3 communication wires.

FIG. 3 illustrates the signal constellation and required comparators for one 2-dimensional PM-II code in accordance with the invention.

FIG. 4 illustrates the signal constellation and required comparators for a second 2-dimensional PM-II code in accordance with the invention.

FIG. 5 illustrates the signal constellation and required comparators for a third 2-dimensional PM-II code in accordance with the invention.

FIG. 6 is a schematic of one embodiment of a driver transmitting three bits on two wires, in accordance with at least one aspect of the invention.

FIG. 7 is a schematic of one comparator embodiment to detect a code transmitting three bits on two wires, in accordance with at least one aspect of the invention.

FIG. 8 shows one embodiment of a decoder which may be combined with the comparators of FIG. 7 to receive and decode three bits transmitted on two wires in accordance with the invention.

FIG. 9 shows the communications channel simulated to produce the results of Table I.

FIG. 10 illustrates a prior art embodiment of a Dynamic Random Access Memory device.

FIG. 11 illustrates a prior art embodiment of one DRAM storage cell as used in the device of FIG. 10.

FIG. 12 is a schematic illustration of prior art connection of sense amplifiers in a DRAM device such as shown in FIG. 10.

FIG. 13 is a schematic illustrating one embodiment of the invention in a DRAM device.

FIG. 14 illustrates the signal constellation and required comparators for a simplified set of comparators mapping groups of 3 bits to codewords.

FIG. 15 is a schematic for one embodiment of an encoder circuit mapping 3 input bits to eight encoded outputs based on the mapping of FIG. 15.

FIG. 16 is a schematic for one embodiment of an output driver for each of the communication wires using the encoding of FIG. 17.

FIG. 17 is a schematic for one embodiment of a decoder based on the mapping of FIG. 15.

DETAILED DESCRIPTION OF THE INVENTION

The use of vector signaling codes offers the possibility of increased pin-efficiency, as well as immunity from common mode and other noise. However, some applications may require vector signaling codes of even higher pin-efficiency. Such applications may, for example, be applications in which single-ended signaling performs fine at a given target transmission rate, but would perform much worse if the transmission rate was increased—for example because of a deep notch in the channel response. Traditionally, practitioners in the field have suggested the use of Pulse Amplitude Modulation (PAM) signaling to increase the pin-efficiency of such a system. PAM is a method of signaling in which the coordinates of a codeword can take one of the values [−1, −1+2/(X−1), . . . , 1−2/(X−1), 1]. This type of signaling is referred to as PAM-X signaling. Often, but not exclusively, X is a power of 2 and each codeword carries log 2(X) (binary logarithm of X) information bits.

One of the disadvantages of PAM-X signaling for large values of X is the need for many fixed references. In such a signaling method, X−1 references must be maintained during operation. In some applications (such as the memory applications discussed below) such references may be difficult to establish. In other applications, such as in chip-to-chip communication, the references may be subject to noise that can erode the signal integrity. Moreover, PAM-X signaling can be sensitive to Intersymbol Interference (ISI) noise, as described in Hormati I.

An alternative type of vector signaling codes is now described in which the receive comparators use at most one reference (called “0” in the following), which have a larger pin-efficiency than normal vector signaling codes, and which can allow for a better immunity to ISI-noise than PAM-X signaling.

A Permutation Modulation vector signaling code of type II (PM-II code, for short) is a vector signaling code in which each codeword is of the form(±c₀,±c₁, .□,c_N-1)wherein (c₀, . . . , c_N-1) is an element of a permutation modulation code generated by a vector x₀. In other words, in this type of coding all permutations of x₀ are used, and the signs of all coordinate positions can be independently modulated.

Detection for PM-II codes can be accomplished using a network of N² comparators. Given the values x₀, x₁, . . . , x_N-1 on the N wires, the list of comparators is given by:

• • N*(N−1)/2 comparators comparing x_i against x_j for 0≦i<j<N.
  • N*(N−1)/2 comparators comparing x_i+x_j against 0 for 0≦i<j<N.
  • N comparators comparing x_i against 0 for 0≦i<N.

FIG. 2 is a schematic of an embodiment of a receive codeword detector as in FIG. 1, in accordance with at least one aspect of the present invention, acting as a detector of a PM-II code on 3 communication wires. The three wires 163 leaving the equalizer unit 162 of FIG. 1 and entering the CMP unit 166 are shown. They carry the values a, b, and c, respectively. The CMP unit comprises 9 comparators 205, 206, . . . , 213, and three adder units 230, implemented in this example as averaging units using two parallel resistors of equal resistance. The comparators 205, 206, 207 and 211, 212, and 213 have one of their legs connected to a fixed reference. The value of that reference depends on the particular values put on the wires. Specifically, comparator 205 compares the value a against ref, comparator 206 compares the value b against ref, and comparator 207 compares the value c against ref. Comparator 211 compares (a+b)/2 against ref, comparator 212 compares (a+c)/2 against ref, and comparator 213 compares (b+c)/2 against ref. Comparators 208, 209, and 210 are differential comparators. They compare a against b, a against c, and b against c, respectively. In some application, the signals entering the CMP unit 166 may have been amplified by an amplifier; alternatively, part of these signals may be amplified before entering the comparators. For example, the signals leaving the adder units 230 may be amplified before entering their respective adder units in order to create a larger vertical opening for the eye diagrams.

In the following, we will give some examples of PM-II codes.

Example 1

2-Dimensional PM-II Code

A 2-dimensional PM-II code is specified by a vector x₀=(a,b). Since the signals on the wires are assumed to be in the interval [−1,1], the parameter a can be assumed to be equal to 1, and b can be assumed to be non-negative.

Described as 2-dimensional vectors, the comparators are (1,−1), (1,1), (1,0) and (0,1), meaning that upon reception of values (x,y) on the wires (after possible equalization), the comparators compare x against y (or x-y against 0), x+y against 0, x against 0, and y against 0.

If b is zero, then the code has 4 elements only, and the codewords are (1,0), (−1,0), (0,1), and (0,−1). The two comparators (1,−1) and (1,1) are sufficient to detect the codewords, so there is no need for the other two comparators. This code has ISI ratio 1. FIG. 3 shows the constellation of these points in the plane, together with the comparators. Specifically, the codewords are the black circles 350, 351, 352, and 353, having coordinates (−1,0), (0,1), (1,0), and (0,−1), respectively. The comparators are shown by the four lines 305, 310, 315, and 320, labeled as (1,0), (1,1), (1,−1), and (0,1), respectively. As can be seen, the comparators (1,−1) and (1,1) are not needed to distinguish the four codewords.

If b is nonzero, then the code has 8 elements. Optimization of the code can be done by minimizing the ISI-ratio:

• • The comparators (1,0) and (0,1) both have ISI-ratio 1/b.
  • The comparators (1,−1) and (−1,1) both have ISI-ratio (1+b)/(1−b) if b is not 1.
    • If b=1, then these comparators are not needed, and the vector signaling code is that of single-ended signaling, as can be seen in FIG. 4. As can be seen, the comparators (1,0) and (0,1) are not needed to distinguish the codewords, shown as black circles.
    • If b is not 1, then the best ISI-ratio is obtained if 1/b=(1+b)/(1−b), which means that b=√{square root over (2)}−1. In this case the codewords are equidistantly distributed on the circle with radius

$\sqrt{4-2\sqrt{2}},$

• • • as shown in FIG. 5. As can be seen from the figure, all four comparators are needed to distinguish the codewords. This code has a pin-efficiency of 1.5, and an ISI-ratio of √{square root over (2)}+1˜2.41.

The exact PM-II code generated by (1, √{square root over (2)}−1) may not be used as is in practice, due to the difficulty of generating a voltage level exactly equal to √{square root over (2)}−1 on the wires. A quantization of this value is therefore desirable. There are various possibilities of quantization, depending on the allowed precision. One possibility would be to replace the quantity √{square root over (2)}−1 by 0.4. The new code, called PM2-2, would then have the codewords

• • (1,0.4), (0.4, 1), (−0.4,1), (−1,0.4),
  • (−1,−0.4), (−0.4,−1), (0.4,−1), (1,−0.4).

The ISI-ratio of the comparators (1,0) and (0,1) for this code are 2.5, and the ISI-ratios of the comparators (1,1) and (1,−1) are 7/3˜2.33. There is thus a slight loss of ISI-ratio for the first two comparators.

No matter what values are chosen for the coordinates of the generating vector in this case, digital logic may be needed to determine which value is transmitted on the two wires. FIG. 6 is an exemplary embodiment of a driver 128 of FIG. 1 sending three bits on two wires. We assume that the three incoming bits are called x, y, z, and we assume that the levels transmitted on the wires are a, b, c, d. In this case the driver may comprise four current sources 605, 606, 607, 608, creating currents of strengths a, b, c, d, respectively. The same current sources are used for both wires 1 and 2, since the coding would never allow the same current to be replicated on both wires. These current sources may be connected to transistors 610, 615, 616, and 617, which are controlled by logical functions of the incoming bits x, y, z. In this exemplary embodiment, the control signals may be NOR(x,z), NOR(x,z), NOR(x,z)=1, and x&z, where x&z is the logical and of x and z, and x is the logical negation of x. This means that the current flowing on wire 1 is equal to a, b, c, or d if NOR(x,z)=1, or NOR(x,z)=1, or NOR(x,z)=1, or x&z=1, respectively. The control logic makes sure that for every combination of the incoming bits exactly one of the current sources opens.

Similarly, the value on the second wire is a, b, c, or d, if NOR(y, x^z)=1, or NOR(y, x^z)=1, or NOR(y, x^z)=1, or y&(x^z)=1, respectively, where u^v indicates the logical XOR of u and v.

FIG. 7 shows the operation of one embodiment of the comparators needed for this coding scheme. In this figure, w1 and w2 are the values on the two wires of the communication system, possibly after an equalization step. These values collectively enter four comparators, which produce digital values A, B, C, and D, respectively. In operation, the first two comparators compare the values w1 and w2 on the two wires against a fixed reference, respectively. The third comparator compares the values w1 and w2. For the fourth comparator, the values on the wires pass two resistors of equal resistance, so that the value at the black dot equals (w1+w2)/2. This value is then compared by the fourth comparator against a fixed reference to obtain the bit D. Where the possible values on the wires are a, b, c, d, the value of the reference is the average (a+b+c+d)/4.

One familiar with the art will note that the multiple input comparators (MIC) taught in Holden I provide an efficient alternative embodiment of the required average calculation and comparison operations. In one embodiment of a MIC, a conventional comparator input circuit is modified by incorporating multiple paralleled transistors on one or both sides of the usual differential amplifier input stage. Scaling of the relative transistor sizes may be used to introduce proportionate factors, as required for an averaging function.

An exemplary embodiment of the operation of a decoder is now described with reference to FIG. 8. The input to this decoder are the four bits A, B, C, D from the four comparators. The output are the bits x, y, z. The bits x and y are equal to A and B, respectively. The decoder comprises two AND gates 820 and 830, inverter 805, an XOR gate 810, and an OR gate 840. The output of the AND gate 830 is (A)&(C^D). The output of the AND gate 820 is C&D. The final output z of the OR gate 840 is (C&D)|(A)&(C^D), where “|” is the OR operation.

Other encodings with reduced complexity decoders are also possible, as illustrated in FIGS. 14-17. In FIG. 14 a mapping from groups of three bits to the codewords is described. FIG. 15 describes a logical circuit which, on input three bits x, y, z, produces 8 outputs A, B, . . . , H. For example, A is equal to NAND(y,z). FIG. 16 describes a driver structure for each of the communication wires. Elements 1601, 1602, 1610, and 1611 are source currents, wherein source currents 1701 and 1710 provide a current of strength √{square root over (2)}−1 and source currents 1602 and 1611 provide a current of strength 1. Similarly, elements 1604 and 1613 are sink currents of strength √{square root over (2)}−1 and elements 1603 and 1612 provide sink currents of strength 1. The source currents are connected to PMOS transistors, whereas the sink currents are connected to NMOS transistors. The control bits for these transistors are given by the outputs of the logical encoder of FIG. 15. An exemplary embodiment of the operation of a decoder is now described with reference to FIG. 17. The input to this decoder are the four bits A, B, C, D from the four comparators. The output are the bits x, y, z. The bits x and y are equal to A and B, respectively. Bit z is equal to the XOR of the outputs of the third and fourth comparator.

Example 2

3-Dimensional PM-II Codes

The generating vector x₀ can be assumed to be of the form (1, a, b) where 1≧a≧b≧0.

• • If b#a, then b can be chosen to be 2−√{square root over (5)} and a can be chosen to be (1+b)/2=(3−√{square root over (5)})/2. This gives a code with 48 codewords, and an ISI-ratio of 2+√{square root over (5)}˜4.24.
  • If b=a, and a≠1, then b can be chosen to be √{square root over (2)}−1. This gives a code with 24 codewords and an ISI-ratio of √{square root over (2)}+1˜2.41. This code has inactives consisting of pairs of codewords and MIC's such that the value of the MIC at that codeword is 0.
  • If b=a=1, then the corresponding code is the 3-dimensional single-ended code, and only three of the comparators are needed to distinguish the codewords.

Reference-Less Vector Signaling Codes from Arbitrary PM-II Codes

PM-II codes as described herein have comparators that compare their values against 0. In fact, up to N*(N+1)/2 such comparators can be of this type. In many high-speed applications, it is desirable to have codewords whose values sum to zero, and comparators that reject common mode noise and are “differential” in the sense that they only compare linear combinations of wire values against one another. In the language of vector signaling codes above, in this setting the codewords c of the vector signaling code should satisfy the property Σ_i=0^N-1c_i=0, and the comparators λ should satisfy Σ_i=0^N-1λ_i=0. For example, permutation modulation codes have this property. In certain applications, however, such permutation modulation codes may not be suitable, for example because their pin-efficiency may not be high enough.

A method is now described to produce reference-less vector signaling codes from PM-II codes. Where a PM-II code of length N is used, the first step of the procedure requires the determination of an orthogonal matrix M of format (N+1)×(N+1). A matrix is called orthogonal if all pairs of distinct rows of the matrix are orthogonal and all rows have Euclidean norm 1. For example, in the matrix below, M below is orthogonal:

$M=\frac{1}{\sqrt{2}}\left(\begin{array}{cc}1& 1\\ 1& -1\end{array}\right).$

In addition to orthogonality, the matrix M needs to satisfy the condition that the sum of all columns of M is an N-dimensional vector that is 0 in all positions except for the first. (Strictly, whether the nonzero position is the first or any other fixed position is irrelevant for the working of this method; the first position was chosen for descriptive purposes.)

Given this matrix, the PM-II code C and the set of MIC's A can be transformed to obtain a vector signaling code that is reference-less and balanced. To accomplish this, the codewords c=(c₀, . . . , c_N-1) of dimension N are transformed to codewords d=(d₀, . . . , d_N) of dimension N+1 via(d₀,d₁, . . . ,d_N)=(0,c₀,c₁, . . . ,c_N-1)*M/L, where the normalization constant L is chosen such that for all the codewords, all the coordinates are between −1 and 1. The MIC's λ=(λ₀, λ₁, . . . , λ_N-1) are transformed to new MIC's μ=(μ₀, μ₁, . . . , μ_N) via(μ₀,μ₁, . . . ,μ_N)=(0,λ₀,λ₁, . . . ,λ_N-1)*M.

As can be verified by inspection, the new codewords are balanced, and the new MIC's are common-mode-resistant. Moreover, since M is orthogonal, the new code has the same ISI-ratio as the old one.

The transformation above is valid for any code with central MIC's, not just PM-II codes.

Example 3

3-Dimensional Balanced Code and its Quantization

We use the PM-II code generated by (1, √{square root over (2)}−1), and use the following orthogonal matrix

$M=\left(\begin{array}{ccc}1/\sqrt{3}& 1/\sqrt{3}& 1/\sqrt{3}\\ 1/\sqrt{2}& -1/\sqrt{2}& 0\\ 1/\sqrt{6}& 1/\sqrt{6}& -2/\sqrt{6}\end{array}\right).$

After scaling, the MIC's become:

• • (1,−1,0),(1,1,−2),(1+√{square root over (3)},1−√{square root over (3)},−2),(−1+√{square root over (3)},−1−√{square root over (3)},2).

The following is a list of the 8 codewords:

• • (−a, 1, −b), (−1, a, b), (1, −a, −b), (a, −1, b),
  • (c, d, −e), (−d, −c, e), (d, c, −e), (−c, −d, e),where a=(√{square root over (3)}−√{square root over (2)}+1)/t, b=2(√{square root over (2)}−1)/t, c=(√{square root over (6)}−√{square root over (3)}−1)/t, d=(√{square root over (6)}−√{square root over (3)}+1)/t,e=2/t, and t=√{square root over (3)}+√{square root over (2)}−1.

This code has pin-efficiency 1, and an ISI-ratio of √{square root over (2)}+1.

In practice it may not be realistic to reproduce the exact values of the codewords on the wires. Quantization can be applied to both the codewords and the MIC's to obtain a simpler vector signaling code with similar properties as the one described here. Many different forms of quantization are possible. For example, if the coordinates of the codewords and the coordinates of the MIC's are to be from 10 different values, the code can be chosen to consist of the codewords

• • ±(0.6,−1,0.4), ±(−0.2, −0.8, 1), ±(−0.8, −0.2, 1), ±(1,−0.6, −0.4),and the MIC's are:
  • (1,−1,0), (0.33, −1, 0.67), (−1, 0.33, 0.67), (0.5, 0.5, −1).

The ISI ratios of these MIC's are 2.67, 2.44, 2.44, and 2.5, respectively.

Example 4

4-Dimensional Balanced Code and its Quantization

Here we will use the PM-II code generated by x₀=(1, √{square root over (2)}−1, √{square root over (2)}−1) of Example 2 together with the Hadamard transform matrix

$M=\frac{1}{2}\left(\begin{array}{cccc}1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& 1& -1& -1\\ 1& -1& -1& 1\end{array}\right).$

There are 9 comparators given in the following:

• • ½(1,−1,1,−1), ½(1,1,−1,−1), ½(1,−1,−1,1),
  • (1,−1,0,0), (1,0,−1,0), (1,0,0,−1),
  • (0,1,−1,0), (0,1,0,−1), (0,0,1,−1).

The 24 codewords, properly normalized to have coordinates between −1 and 1, are given in the following:

• • (a, −c, −c, b), (c, −b, −a, c), (c, −a, −b, c), (b, −c, −c, a), (−b, c, c, −a), (−c, a, b, −c),
  • (−c, b, a, −c), (−a, c, c, −b), (a, b, −c, −c), (c, c, −a, −b), (−b, −a, c, c), (−c, −c, b, a),
  • (c, c, −b, −a), (b, a, −c, −c), (−c, −c, a, b), (−a, −b, c, c), (a, −c, b, −c), (−b, c, −a, c),
  • (c, −a, c, −b), (−c, b, −c, a), (c, −b, c, −a), (−c, a, −c, b), (b, −c, a, −c), (−a, c, −b, c)where a=1, b=(−5+4√{square root over (2)})/7˜0.094, and c=(1+2√{square root over (2)})/7˜0.547.

This code has an alphabet of size 6, has 24 codewords, and an ISI-ratio of √{square root over (2)}+1. It is therefore better than the quaternary PM-code generated by the vector(1,⅓,−⅓,−1) which also has 24 codewords, but a worse ISI-ratio of 3.

Table I below has been compiled using statistical eye diagram software developed by the company Kandou Bus. The channel setup is given in FIG. 9. It comprises a chip board 905 consisting of a chip wire-bonded to a short stretch of stripline on the chip board. The striplines are connected via cables to a channel board 910 containing 472 mm of stripline on a Rogers material. These striplines are connected again via cables to another chip board 920 consisting of connectors and a stripline and eventually connected with another chip which is wire-bonded with the chip board. The channel has been extracted from a real model using a vector network analyzer. The following table shows the horizontal opening of the worst eye for various UI rates per wire. The third column is the horizontal opening for the PM-II code described here, and the last column shows the horizontal opening for the PM code generated by the vector (1,⅓,−⅓,−1). The numbers are in pico-seconds. As can be seen, the lower ISI-ratio of the PM-II code results in a larger horizontal opening.

TABLE I
UI rate per
wire in GHz	PM-II	PM
1	660	600
2	320	285
3	206	183
4	145	127
5	110	94
6	88	73
7	68	57
8	56	42
9	46	35
10	38	28
11	32	24
12	26	18
13	24	17
14	17	11
15	16	10

In practice, it may be difficult to create the exact values for b and c on the wires. The ISI-ratio is somewhat robust to slight variations of these choices. For example, choosing b=0.1 and c=0.55, the ISI-ratios of the first 3 comparators become 22/9˜2.44 and the ISI-ratios of the other 6 comparators become 31/13˜2.39. Simulation of this code does not reveal any noticeable difference in terms of the horizontal and vertical opening compared to the original code. Other quantizations are also possible, as is evident to those of skill in the art.

Example 5

Reduced Number of Comparators

Teachings of Shokrollahi I can be used to reduce the number of comparators of the vector signaling code in Example 4 by reducing the set of codewords accordingly. The following examples are compiled using those methods.

Example 5.1

8 Codewords and 3 Comparators

The following 8 codewords

• • (−1, c, −b, c), (1, −c, b, −c), (c, c, −b, −1), (−c, −c, b, 1),
  • (−c, b, 1, −c), (c, −1, −b, c), (c, −b, −1, c), (−c, 1, b, −c)and the following three comparators
  • (1,0,−1,0), (0,1,−1,0), (0,0,−1,0)define a vector signaling code with ISI ratio √{square root over (2)}+1. The number of comparators is obviously optimal.

Example 5.2

12 Codewords and 4 Comparators

The following 12 codewords

• • (−1, c, −b, c), (b, −c, 1, −c), (−c, 1, −c, b), (c, −b, c, −1), (−c, b, −c, 1), (−b, c, −1, c),
  • (1, −c, b, −c), (−c, b, 1, −c), (−b, c, c, −1), (c, −1, −b, c), (c, −b, −1, c), (c, −1, c, −b)and the following four comparators
  • (1,1,−1,−1)/2, (1,−1,−1,1)/2, (1,−1,0,0), (0,0,−1,1)define a vector signaling code of ISI ratio √{square root over (2)}+1.

Example 5.3

16 Codewords and 5 Comparators

The following 16 codewords

• • (c, c, −b, −1), (−1, −b, c, c), (−c, −c, 1, b), (b, 1, −c, −c), (1, −c, −c, b), (−c, −c, b, 1),
  • (−b, −1, c, c), (c, c, −1, −b), (−1, c, c, −b), (−c, b, 1, −c), (−c, 1, b, −c), (−b, c, c, −1),
  • (b, −c, −c, 1), (c, −1, −b, c), (c, −b, −1, c), (1, b, −c, −c),and the following five comparators
  • (1,−1,1,−1)/2, (1,1,−1,−1)/2, (1,−1,−1,1)/2, (1,0,−1,0), (0,1,0,−1)define a vector signaling code of ISI ratio √{square root over (2)}+1.

Applications to the design of dense dynamic random access memory (DRAM)

Permutation modulation codes of type 2 can also be used for more efficient storage of bits in dynamic random access memory (DRAM) chips. Efficient storage of data in DRAM's has been the subject of much investigation. In particular, Cronie IV describes methods for DRAM storage that lead to higher density and increased noise resilience. The methods of Cronie IV are for the most part based on permutation modulation codes. The use of permutation modulation codes of type 2 will allow for higher storage density in a group of DRAM cells of a given size, as will be explained below.

FIG. 10 is an exemplary block diagram schematic of a conventional DRAM storage device. Briefly, a conventional DRAM storage device comprises a column decoder 1030, I/O buffers 1020, sense amplifiers 1045, row decoders 1010, and a memory area 1050. The memory area contains the actual memory cells 1035. These memory cells 1035 are connected via bitlines 1033, to the sense amplifiers 1045 and the column decoder 1030, and, via wordlines 1050, to associated memory cells 1035 and to row decoders 1010. In operation, to write to a memory cell, the row and the column address of the cell is selected by the column and row decoders 1030 and 1010. Here, the data to be stored is received by the I/O buffers 1020 and stored into a selected memory cell via the sense amplifiers 1045. The chip's on-board logic charges the cell capacitance or discharges it, using the bitlines and the wordlines.

The structure of a conventional DRAM memory cell 1035 is further highlighted in FIG. 11. It consists of a transistor 1130 and a capacitor 1150. The capacitor stores a charge that corresponds directly to the data state of the data input to the I/O buffers 1020. When wordline 1050 is activated, during a write operation, the charge is transferred to the bitline 1033. The charge stored in memory cell 1035 is used to determine the “value” stored therein. In this regard, with reference to FIG. 12, bitlines 1220 are pre-charged to V_dd/2. The bitlines on the group of bits on the right hand side of the figure will be read by opening the wordlines 1212, 1214, and 1216, and the difference of the charge to the pre-charged values of bitlines 1220 are measured by the sense amplifiers 1250. These readings are then forwarded to the row decoders for obtaining the bit values in each cell. Thus, in conventional DRAM memory, each memory cell 1035 stores a charge in and outputs a charge from the associated capacitor 1150 which corresponds directly to the value of the data received by and output from the I/O buffers 1020.

A different DRAM structure is now disclosed using the example of the code PM2-2 of Example 1 above. The particular quantization chosen in this code is not important for the working of this disclosure and other quantizations that lead to the same number of codewords and comparators work in the same way.

This embodiment, shown in FIG. 13, incorporates a memory area 1040 as in FIG. 10. However, the DRAM cells in this embodiment's memory area are grouped into sets of 2 adjacent cells each, which are written and read together. For each such group, there are 4 (instead of 2) sense amplifiers 1301, 1302, 1303, and 1304. Sense amplifiers 1303 and 1304 are as before. Sense amplifier 1302 in effect measures the average of the values on bitlines 1340 and 1345 using the resistors 1330 of equal resistance, against the average of the values on bitlines 1350 and 1355, precharged to V_dd/2, as described above. This average is computed using a similar pair 1320 of resistors on these bitlines. Sense amplifier 1301 measures the values of the bitlines 1340 and 1345 against one another. In an alternative embodiment, the multi-input comparators of Holden I may be used to calculate the average values and perform their comparison functions without the introduction of additional resistors into the sense amplifier input path.

The values of these sense amplifiers are forwarded to the column decoder unit 1030. This unit may include the decoding logic 1890 of FIG. 18, or any other logic that can uniquely recover the 3 bits from the four sense amplifier measurements.

The number of DRAM cells in a group and the number of sense amplifiers are given for descriptive purposes, and do not imply a limitation. It will be apparent to one familiar with the art that the described method be applied to groups of DRAM cells greater than two, and sets of sense amplifiers greater than four to support different numbers of bits being stored per DRAM cell group.

Claims

1. A method comprising: obtaining a Permutation Modulation Variant II code (PM II code) of length N;determining an orthogonal matrix M of format (N+1)×(N+1), wherein the sum of all the columns in the matrix M is 0, except for one;transforming the PM-II code using the orthogonal matrix M to obtain a reference-less, balanced vector signaling code, wherein the reference-less, balanced vector signaling code is normalized such that each element is between 1 and −1; andtransmitting the reference-less, balanced vector signaling code.

2. The method of claim 1, wherein the pin efficiency of the PM-II code is at least 1.5.

3. The method of claim 1, wherein each codeword of the PM-II code has at least 2 elements.

4. The method of claim 1, wherein the reference-less, balanced vector signaling code has an equal inter-symbol interference USD ration equal to the PM-II code.

5. The method of claim 1, wherein the reference-less, balanced vector signaling code is at least ternary.

6. The method of claim 1, further comprising receiving, at a set of common-mode resistant multi-input comparators (MICs), N+1 elements of a codeword, and responsively generating a set of comparator outputs.

7. The method of claim 6, wherein the set of common-mode resistant MICs comprises N+1 MICs.

8. The method of claim 7, wherein the set of common-mode resistant MICs comprises fewer than N+1 MICs.

9. The method of claim 6, wherein each MIC receives the N+1 elements of the codeword.

10. The method of claim 6, wherein at least two of the MICs are mutually orthogonal.

11. An apparatus comprising: an encoder configured to obtain a Permutation Modulation Variant II code (PM-II code) of length N, to determining an orthogonal matrix M of format (N+1)×(N+1), wherein the sum of all the columns in the matrix M is 0, except for one, and to transform the PM-II code using the orthogonal matrix M to obtain a reference-less, balanced vector signaling code, wherein the reference-less, balanced vector signaling code is normalized such that each element is between 1 and −1; anda transmit driver configured to transmit the reference-less, balanced vector signaling code over a multi-wire bus.

12. The apparatus of claim 11, wherein the pin efficiency of the PM-II code is at least 1.5.

13. The apparatus of claim 11, wherein each codeword of the PM-II code has at least 2 elements.

14. The apparatus of claim 11, wherein the reference-less, balanced vector signaling code has an equal inter-symbol interference USD ration equal to the PM-II code.

15. The apparatus of claim 11, wherein the reference-less, balanced vector signaling code is at least ternary.

16. The apparatus of claim 11, further comprising a set of common-mode resistant multi-input comparators (MICs) configured to receive N+1 elements of a codeword and to generate a set of comparator outputs.

17. The apparatus of claim 16, wherein the set of common-mode resistant MICs comprises N+1 MICs.

18. The apparatus of claim 17, wherein the set of common-mode resistant MICs comprises fewer than N+1 MICs.

19. The apparatus of claim 16, wherein each MIC receives the N+1 elements of the codeword.

20. The apparatus of claim 16, wherein at least two of the MICs are mutually orthogonal.