Orthogonal differential vector signaling codes with embedded clock

Information

  • Patent Grant
  • 10652067
  • Patent Number
    10,652,067
  • Date Filed
    Monday, November 5, 2018
    5 years ago
  • Date Issued
    Tuesday, May 12, 2020
    4 years ago
Abstract
Orthogonal differential vector signaling codes are described which support encoded sub-channels allowing transport of distinct but temporally aligned data and clocking signals over the same transport medium. Embodiments providing enhanced LPDDR interfaces are described which are suitable for implementation in both conventional high-speed CMOS and DRAM integrated circuit processes.
Description
REFERENCES

The following references are herein incorporated by reference in their entirety for all purposes:


U.S. Patent Publication No. 2011/0268225 of U.S. patent application Ser. No. 12/784,414, filed May 20, 2010, naming Harm Cronie and Amin Shokrollahi, entitled “Orthogonal Differential Vector Signaling”, hereinafter identified as [Cronie I];


U.S. patent application Ser. No. 13/030,027, filed Feb. 17, 2011, naming Harm Cronie, Amin Shokrollahi and Armin Tajalli, entitled “Methods and Systems for Noise Resilient, Pin-Efficient and Low Power Communications with Sparse Signaling Codes”, hereinafter identified as [Cronie II];


U.S. patent application Ser. No. 14/158,452, filed Jan. 17, 2014, naming John Fox, Brian Holden, Peter Hunt, John D Keay, Amin Shokrollahi, Richard Simpson, Anant Singh, Andrew Kevin John Stewart, and Giuseppe Surace, entitled “Chip-to-Chip Communication with Reduced SSO Noise”, hereinafter identified as [Fox I];


U.S. patent application Ser. No. 13/842,740, filed Mar. 15, 2013, naming Brian Holden, Amin Shokrollahi and Anant Singh, entitled “Methods and Systems for Skew Tolerance in and Advanced Detectors for Vector Signaling Codes for Chip-to-Chip Communication”, hereinafter identified as [Holden I];


U.S. Provisional Patent Application No. 61/934,804, filed Feb. 2, 2014, naming Ali Hormati and Amin Shokrollahi, entitled “Methods for Code Evaluation Using ISI Ratio”, hereinafter identified as [Hormati I];


U.S. Provisional Patent Application No. 61/934,807, filed Feb. 2, 2014, naming Amin Shokrollahi, entitled “Vector Signaling Codes with High pin-efficiency and their Application to Chip-to-Chip Communications and Storage”, hereinafter identified as [Shokrollahi I];


U.S. Provisional Patent Application No. 61/839,360, filed Jun. 23, 2013, naming Amin Shokrollahi, entitled “Vector Signaling Codes with Reduced Receiver Complexity”, hereinafter identified as [Shokrollahi II].


U.S. Provisional Patent Application No. 61/946,574, filed Feb. 28, 2014, naming Amin Shokrollahi, Brian Holden, and Richard Simpson, entitled “Clock Embedded Vector Signaling Codes”, hereinafter identified as [Shokrollahi III].


U.S. Provisional Patent Application No. 62/015,172, filed Jul. 10, 2014, naming Amin Shokrollahi and Roger Ulrich, entitled “Vector Signaling Codes with Increased Signal to Noise Characteristics”, hereinafter identified as [Shokrollahi IV].


U.S. patent application Ser. No. 13/895,206, filed May 15, 2013, naming Roger Ulrich and Peter Hunt, entitled “Circuits for Efficient Detection of Vector Signaling Codes for Chip-to-Chip Communications using Sums of Differences”, hereinafter identified as [Ulrich I].


U.S. Provisional Patent Application No. 62/026,860, filed Jul. 21, 2014, naming Roger Ulrich and Amin Shokrollahi, entitled “Bus Reversible Orthogonal Differential Vector Signaling Codes”, hereinafter identified as [Ulrich II].


The following additional references to prior art have been cited in this application:


U.S. Pat. No. 7,053,802, filed Apr. 22, 2004 and issued May 30, 2006, naming William Cornelius, entitled “Single-Ended Balance-Coded Interface with Embedded-Timing”, hereinafter identified as [Cornelius];


U.S. Pat. No. 8,064,535, filed Mar. 2, 2007 and issued Nov. 22, 2011, naming George Wiley, entitled “Three Phase and Polarity Encoded Serial Interface, hereinafter identified as [Wiley].


U.S. Pat. No. 8,649,460, filed Mar. 11, 2010 and issued Feb. 11, 2014, naming Frederick Ware and Jade Kizer, entitled “Techniques for Multi-Wire Encoding with an Embedded Clock”, hereinafter identified as [Ware].


BACKGROUND

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.


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. 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. When transmitted as physical signals on a communications medium, symbols may be represented by particular physical values appropriate to that medium; as examples, in one embodiment a voltage of 150 mV may represent a “+1” symbol and a voltage of 50 mV may represent a “−1” symbol, while in another embodiment “+1” may be represented by 800 mV and “−1” as −800 mV.


A vector signaling code, as described herein, is a collection C of vectors of the same length N, called codewords. 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. The Orthogonal Differential Vector Signaling codes of [Cronie I], [Cronie II], [Fox I], [Shokrollahi I], [Shokrollahi II], and [Shokrollahi III] are examples of vector signaling codes, and are used herein for descriptive purposes.



FIG. 1 illustrates a communication system employing vector signaling codes. Bits S0, S1, S2 enter block-wise 100 into an encoder 105. The size of the block may vary and depends on the parameters of the vector signaling code. The encoder generates a codeword of the vector signaling code for which the system is designed. In operation, the encoder may generate information used to control PMOS and NMOS transistors within driver 110, generating voltages or currents on the N communication wires 125 comprising the communications channel 120. Receiver 132 reads the signals on the wires, possibly including amplification, frequency compensation, and common mode signal cancellation. Receiver 132 provides its results to decoder 138, which recreates the input bits at 140, here shown as received bits R0, R1, R2.


Depending on which vector signaling code is used, there may be no decoder, or no encoder, or neither a decoder nor an encoder. For example, for the 8b8w code disclosed in [Cronie II], both encoder 112 and decoder 1138 exist. On the other hand, for the Hadamard code disclosed in [Cronie I], an explicit decoder may be unnecessary, as the system may be configured such that receiver 132 generates output bits 140 directly.


The operation of the transmitting device 110, comprising input data 100 and elements 112 and 118, and that of the receiving device 130, including element 132, optional element 138, and output data 140, have to be completely synchronized in order to guarantee correct functioning of the communication system. In some embodiments, this synchronization is performed by an external clock shared between the transmitter and the receiver. Other embodiments may combine the clock function with one or more of the data channels, as in the well-known Biphase encoding used for serial communications.


One important example is provided by memory interfaces in which a clock is generated on the controller and shared with the memory device. The memory device may use the clock information for its internal memory operations, as well as for I/O. Because of the burstiness and the asynchronicity of memory operations, the I/O may not be active all the time. Moreover, the main clock and the data lines may not be aligned due to skew. In such cases, additional strobe signals are used to indicate when to read and write the data.


BRIEF DESCRIPTION

Orthogonal differential vector signaling codes providing transport for both data and a clocking signal are described which are suitable for implementation in both conventional high-speed CMOS and DRAM integrated circuit processes. Example channels derived from current practice for Low-Powered DDR4 interfaces are described, as are modest channel enhancements providing higher speed and greater signal integrity.





BRIEF DESCRIPTION OF FIGURES


FIG. 1 illustrates a communication system employing vector signaling codes.



FIG. 2 illustrates one embodiment of an ODVS communications system in which a discrete decoding function is not required.



FIG. 3 is a block diagram of an embodiment transporting data and a clock signal using ODVS code, and incorporating elements facilitating integration of the receiver with conventional DRAM practice.



FIG. 4 is a block diagram of an embodiment utilizing 5b6w code, also known as Glasswing, to implement transport over a proposed LPDDR5 channel.



FIG. 5 is a block diagram of an embodiment utilizing 8b9w code to implement transport over a proposed LPDDR5 channel.



FIG. 6 is a block diagram of an embodiment utilizing ENRZ code to implement transport over a proposed LPDDR5 channel.



FIGS. 7A, 7B, and 7C shows comparative receive eye diagrams for Glasswing, ENRZ, and 8b9w embodiments, respectively, operating at 6.4 GBaud and 8.4 GBaud signaling rates.



FIG. 8 depicts a process in accordance with at least one embodiment.





DETAILED DESCRIPTION


FIG. 1 illustrates a communication system employing vector signaling codes. Source data to transmitter 110, herein illustrated as S0, S1, S2 enter block-wise 100 into encoder 112. The size of the block may vary and depends on the parameters of the vector signaling code. The encoder 112 generates a codeword of the vector signaling code for which the system is designed. In operation, the codeword produced by encoder 112 is used to control PMOS and NMOS transistors within driver 118, generating two, three, or more distinct voltages or currents on each of the N communication wires 125 of communications channel 120, to represent the N symbols of the codeword. Within communications receiver 130, receiver 132 reads the voltages or currents on the N wires 125, possibly including amplification, frequency compensation, and common mode signal cancellation, providing its results to decoder 138, which recreates the input bits as received results 140, herein shown as R0, R1, R2. As will be readily apparent, different codes may be associated with different block sizes and different codeword sizes; for descriptive convenience and without implying limitation, the example of FIG. 1 illustrates a system using an ODVS code capable of encoding a three binary bit value for transmission over four wires, a so-called 3b4w code.


Depending on which vector signaling code is used, there may be no decoder, or no encoder, or neither a decoder nor an encoder. For example, for the 8b8w code disclosed in [Cronie II], both encoder 112 and decoder 138 exist. On the other hand, for the H4 code disclosed in [Cronie I] (also described herein as ENRZ,) an explicit decoder may be unnecessary, as the system may be configured such that receiver 132 generates the received results 140 directly.


The operation of the communications transmitter 110 and communications receiver 130 have to be completely synchronized in order to guarantee correct functioning of the communication system. In some embodiments, this synchronization is performed by an external clock shared between the transmitter and the receiver. Other embodiments may combine the clock function with one or more of the data channels, as in the well-known Biphase encoding used for serial communications.


One important example is provided by memory interfaces in which a clock is generated on the controller and shared with the memory device. The memory device may use the clock information for its internal memory operations, as well as for I/O. Because of the burstiness and the asynchronicity of memory operations, the I/O may not be active all the time. Moreover, the main clock and the data lines may not be aligned due to skew. In such cases, additional strobe signals are used to indicate when to read and write the data.


The interface between a system memory controller and multiple Dynamic RAM devices has been well optimized over multiple design generations for both transfer speed and low power consumption. The present state of the art DRAM interface, LPDDR4, includes 8 data lines, 1 DMI signal, 2 strobe lines, as well as other non-data-transfer related lines.


There is considerable interest in extending LPDDR4 to support higher performance at equal or less power consumption, but simple performance extrapolations of the existing technology seem problematic. Decreasing signal integrity precludes simply raising data transfer rates using the existing single-ended interconnection, and misalignment of received DRAM data and its strobe signal is a known issue even at current clock speeds. However, introduction of new technology is constrained by a strong desire to retain as much of the conventional practice as possible regarding bus layout, signal distribution, clocking, etc., as well as a hard requirement that the new technology be implementable in both the high-speed CMOS process used for memory controllers, and in the highly specialized DRAM fabrication process which produces extremely small, high capacitance and low leakage memory cells, but comparatively slow digital and interface logic.


Because of this slow logic speed, conventional DRAM designs utilize two or more phases of processing logic to handle the current LPDDR4 data transfer rates, as one example using one phase of processing logic to capture data on the rising edge of the data transfer strobe, and another phase of processing logic to capture data on the falling edge of the strobe. One hidden limitation of such multi-phased processing embodiments is the difficulty of extracting difference-based information from consecutively received unit intervals, as consecutive unit intervals by definition are known only by different processing phases. Thus, multi-phased processing is problematic for both codes using transition-encoding, as well as embedded- or self-clocking data solutions that rely on comparison of data values received in consecutive unit intervals.


These issues of clock extraction, and transition- or change-detection are most intractable in the communications receiver embodiment, thus the examples herein focus on embodiments in which the relatively slow DRAM device is the receiver. No limitation is implied, as one familiar with the art will readily acknowledge that bidirectional data communication with DRAM devices is well understood, and that any example embodiment suitable for DRAM receive implementation could easily implement the simpler transmit requirements as well.


Receivers Using Multi-Input Comparators


As described in [Holden I], a multi-input comparator with coefficients a0, a1, . . . , am-1 is a circuit that accepts as its input a vector (x0, x1, . . . , xm-1) and outputs

Result=(a0*x0+ . . . +am-1*xm-1)  (Eqn. 1)


In many embodiments, the desired output is a binary value, thus the value Result is sliced with an analog comparator to produce a binary decision output. Because this is a common use, the colloquial name of this circuit incorporates the term “comparator”, although other embodiments may use a PAM-3 or PAM-4 slicer to obtain ternary or quaternary outputs, or indeed may retain the analog output of Eqn. 1 for further computation. In at least one embodiment, the coefficients are selected according to sub-channel vectors corresponding to rows of a non-simple orthogonal or unitary matrix used to generate the ODVS code.


As one example, [Ulrich I] teaches that the ODVS code herein called ENRZ may be detected using three instances of the same four input multi-input comparator, performing the operations

R0=(A+C)−(B+D)  (Eqn. 2)
R1=(C+D)−(A+B)  (Eqn. 3)
R2=(C B)−(D+A)  (Eqn. 4)

which may be readily performed with three identical instances of a multi-input comparator with coefficients of [+1 +1 −1 −1] and distinct permutations of the four input values as described in Eqn. 2-4.


ODVS Sub-Channels


It is conventional to consider the data input to encoder 112 of FIG. 1 as vectors of data (i.e., a data word) to be atomically encoded as a codeword to be transmitted across channel 120, detected by receiver 132, and ultimately decoded 138 to produce a received reconstruction of the transmitted vector or data word.


However, it is equally accurate to model the communications system in a somewhat different way. As this alternate model is most easily understood in a system not requiring a separate decoder, a particular embodiment based on the ENRZ code as illustrated in FIG. 2 will be used for purposes of description, with no limitation being implied. Elements in FIG. 2 functionally identical to elements of FIG. 1 are identically numbered, although FIG. 2 may subsequently illustrate additional internal structure or composition of features that are generically described in FIG. 1


In FIG. 2, input data vector 100 entering communications transmitter 110 is explicitly shown to be expanded to its individual bits S0, S1, S2 and entering encoder 112. Individual signals representing the symbols of the codeword output by encoder 112 are shown controlling individual line drivers 118 to emit signals onto wires 125 comprising communications channel 120. As any one wire transporting the ENRZ code can take on one of four different signal values, two control signals are shown controlling each wire's line driver.


As previously noted, in this embodiment communications receiver 130 does not require an explicit decoder. The internal structure of receiver 132 is illustrated, comprising four receive front ends (as 131) that accept signals from wires 125, and optionally may include amplification and equalization, as required by the characteristics of the communications channel 120. Three multi-input comparators are shown with their inputs connected to the four received wire signals as described by Eqns. 2, 3, and 4. For avoidance of confusion, the multi-input comparators are illustrated as including a computational function 133 followed by a slicing function 134 producing digital outputs R0, R1, R2 from the computational combination of the input values.


One familiar with the art may note that the ODVS encoder accepts one set of input data and outputs one codeword per transmit unit interval. If, as is the case in many embodiments, the encoder includes combinatorial digital logic (i.e. without additional internal state,) this periodic codeword output may easily be seen as performing a sampling function on the input data followed by the encoding transformation, subsequent transmission, etc. Similarly, if the detection operation within the receiver is similarly combinatorial, as is the case here with multi-input comparators performing the detection, the state of a given output element is solely determined by the received signal levels on some number of channel wires. Thus, each independent signal input (as one example, S0) and its equivalent independent signal output (as R0) may be considered a virtual communications channel, herein called a “sub-channel” of the ODVS encoded system. A given sub-channel may be binary (i.e. communicate a two-state value) or may represent a higher-ordered value. Indeed, as taught by [Shokrollahi IV], the sub-channels of a given ODVS code are sufficiently independent that they may utilize different alphabets (and sizes of alphabets) to describe the values they communicate.


All data communications in an ODVS system, including the state changes in sub-channels, are communicated as codewords over the entire channel. An embodiment may associate particular mappings of input values to codewords and correlate those mappings with particular detector results, as taught by [Holden I] and [Ulrich I], but those correlations should not be confused with partitions, sub-divisions, or sub-channels of the communications medium itself


The concept of ODVS sub-channels is not limited by the example embodiment to a particular ODVS code, transmitter embodiment, or receiver embodiment. Encoders and/or decoders maintaining internal state may also be components of embodiments. Sub-channels may be represented by individual signals, or by states communicated by multiple signals.


Timing Information on a Sub-Channel


As an ODVS communications system must communicate each combination of data inputs as encoded transmissions, and the rate of such encoded transmissions is of necessity constrained by the capacity of the communications medium, the rate of change of the data to be transmitted must be within the Nyquist limit, where the rate of transmission of codewords represents the sampling interval. As one example, a binary clock or strobe signal may be transmitted on an ODVS sub-channel, if it has no more than one clock edge per codeword transmission.


An embodiment of an ODVS encoder and its associated line drivers may operate asynchronously, responding to any changes in data inputs. Other embodiments utilize internal timing clocks to, as one example, combine multiple phases of data processing to produce a single high-speed output stream. In such embodiments, output of all elements of a codeword is inherently simultaneous, thus a strobe or clock signal being transported on a sub-channel of the code will be seen at the receiver as a data-aligned clock (e.g. with its transition edges occurring simultaneous to data edges on other sub-channels of the same code.) Similar timing relationships are often presumed in clock-less or asynchronous embodiments as well.



FIG. 3 is a block diagram of an ODVS communications system, in which a data-aligned strobe signal (comparable to the strobe associated with known LPDDR4 channels) is carried by a sub-channel, and N bits of data are carried on other sub-channels of the same code. At the receiver, a collection of multi-input comparators 132 detects the received information, outputting data 345 and a received data-aligned strobe 346. Introduction of a one-half unit interval time delay 350 offsets the received strobe to produce an eye-aligned strobe 356 having a transition edge at the optimum sampling time to latch data 345. As is conventional in many DRAM embodiments, two processing phases are shown for data sampling; phase 360 sampling data 345 on the negative edge of eye-aligned strobe 356, and phase 370 sampling data 345 on the positive edge of eye-aligned strobe 356. Methods of embodiment for delay 350 as well as any associated adjustment or calibration means it may require is well known in the art for LPDDR interfaces.


Mapping LPDDR Communications to an ODVS System


The existing LPDDR4 specification provides for eight data wires, one wire for DMI, and two Strobe wires, for a total of 11 wires. These legacy connections may be mapped to a new protocol mode, herein called LPDDR5, using ODVS encoding in several ways.


As taught by [Holden I], the noise characteristics of a multi-input comparator are dependent on its input size and configuration. [Shokrollahi IV] also teaches that the signal amplitudes resulting from various computations as Eqn. 1 can present different receive eye characteristics. Thus, preferred embodiments will designate a higher quality (e.g. wider eye opening) sub-channel to carry clock, strobe, or other timing information, when the characteristics of the available sub-channels vary.


Glasswing


A first embodiment, herein identified as Glasswing and shown in the block diagram of FIG. 4, adds a new wire to provide a total of 12 wires that are then logically divided into two groups of six wires each. Each group of six wires is used to carry an instance of an ODVS code transmitting 5 bits on 6 wires (called the 5b6w code henceforth), thus providing a total of ten sub-channels. Eight sub-channels are used to carry eight bits of data, one sub-channel is used to carry a mask bit (conventionally used during DRAM write operations to block individual byte writes), and one sub-channel is used to carry a data-aligned strobe. The 5b6w code is balanced, all symbols within any given codeword summing to zero, and is structured such that each codeword contains exactly one +1 and one −1, the remaining codeword symbols being including +⅓ and −⅓ symbols. As will be apparent to one familiar with the art, multiple permutations of a suitable codeword set and corresponding comparator detection coefficients may be used in embodiments.


Each 5b6w receiver in Glasswing incorporates five multi-input comparators. In a preferred embodiment, the codewords of each instance of the 5b6w code are shown in Table 1 and the set of comparators are:

x0−x1
(x0+x1)/2−x2
x4−x5
x3−(x4+x5)/2
(x0+x1+x2)/3−(x3+x4+x5)/3

where the wires of each six wire group are designated as x0, x1 . . . x5.












TABLE 1









±[1, ⅓, −⅓, −1, −⅓, ⅓]
±[1, ⅓, −⅓, ⅓, −1, −⅓]



±[⅓, 1, −⅓, −1, −⅓, ⅓]
±[⅓, 1, −⅓, ⅓, −1, −⅓]



±[⅓, −⅓, 1, −1, −⅓, ⅓]
±[⅓, −⅓, 1, ⅓, −1, −⅓]



±[−⅓, ⅓, 1, −1, −⅓, ⅓]
±[−⅓, ⅓, 1, ⅓, −1, −⅓]



±[1, ⅓, −⅓, −1, ⅓, −⅓]
±[1, ⅓, −⅓, ⅓, −⅓, −1]



±[⅓, 1, −⅓, −1, ⅓, −⅓]
±[⅓, 1, −⅓, ⅓, −⅓, −1]



±[⅓, −⅓, 1, −1, ⅓, −⅓]
±[⅓, −⅓, 1, ⅓, −⅓, −1]



±[−⅓, ⅓, 1, −1, ⅓, −⅓]
±[−⅓, ⅓, 1, ⅓, −⅓, −1]










Additional information about this 5b6w code is provided in [Ulrich II].


8b9w


A second embodiment, herein identified as “8b9w” and shown in the block diagram of FIG. 5, retains the existing LPDDR4 compliment of 11 data transfer wires. Nine wires are used to carry an 8b9w code internally including a 5 wire code herein called the 4.5b5w code and a 4 wire code herein called the 3.5b4w code, which combined provides 288 distinct codeword combinations of which 257 will be used by the encoder. 256 of the codewords are used to encode 8 bits of data when the Mask input is false, and one codeword is used to mark a “do not write” condition when the Mask input is true. A data-aligned strobe is communicated using legacy means, using the two existing LPDDR4 strobe wires.


In at least one embodiment, each 4.5b5w receiver incorporates seven multi-input comparators, using the codewords of the 4.5b5w code as given in Table 2 and the set of comparators

x0−x1
x0−x2
x0−x3
x1−x2
x1−x3
x2−x3
(x0+x1+x2+x3)/4−x4

where the wires of each five wire group are designated as x0, x1 . . . x4.












TABLE 2









±[0, −1, 1, 1, −1]
±[−1, 1, 0, 1, −1]



±[0, 1, −1, 1, −1]
±[1, −1, 0, 1, −1]



±[0, 1, 1, −1, −1]
±[1, 1, 0, −1, −1]



±[−1, 0, 1, 1, −1]
±[−1, 1, 1, 0, −1]



±[1, 0, −1, 1, −1]
±[1, −1, 1, 0, −1]



±[1, 0, 1, −1, −1]
±[1, 1, −1, 0, −1]










The ISI-ratio of the first 6 comparators (as defined in [Hormati I]) is 2, whereas the ISI-ratio of the last comparator is 1.


In the same embodiments, the codewords of the 3.5b4w code are given in Table 3.












TABLE 3









±[1, −1, 0, 0]
±[0, 1, −1, 0]



±[1, 0, −1, 0]
±[0, 1, 0, −1]



±[1, 0, 0, −1]
±[0, 0, 1, −1]










Each 3.5b4w receiver incorporates six multi-input comparators. If the wires of each four wire group are designated as x0, x1 . . . x3, the comparators are:

x0−x1
x0−x2
x0−x3
x1−x2
x1−x3
x2−x3


The ISI-ratio of all these comparators (as defined in [Hormati I]) is 2.


ENRZ


A third embodiment, herein identified as “ENRZ” and shown in the block diagram of FIG. 6, adds a new wire to the existing LPDDR4 compliment to provide a total of 12 wires that are then logically divided into three groups of four wires each. Each group of four wires is used to carry an instance of ENRZ code, each instance thus having eight unique codewords. In at least one embodiment, one codeword from each instance is reserved as a repeat code, with the seven remaining codewords per instance being combined by the encoder to provide 7*7*7=343 unique combinations, more than sufficient to encode eight data bits and a mask condition, as in the previous example. In another embodiment, there is no designated repeat codeword. Instead, the transmitter may store the last transmitted codeword, and produce for the following UI a codeword that is different from the transmitted one, as taught in [Shokrollahi III]. The Data-aligned strobe is used to clock codeword emission at the transmitter, with the repeat code being emitted on each instance whenever the present codeword to be emitted is identical to the codeword emitted in the previous unit interval. At the receiver, a known art clock recover circuit extracts timing information from received codeword edges, and a one data value history buffer regenerates duplicated data values for each instance on detection of a received repeat codeword.


Further description of this embodiment may be found in [Shokrollahi III].



FIGS. 7A, 7B, and 7C provide a comparison of the various embodiments; with receive eye diagrams shown for Glasswing, ENRZ, and 8b9w embodiments, respectively, at signaling rates of 6.4 GBaud and 8.4 GBaud.


The examples presented herein illustrate the use of vector signaling codes for point-to-point wire communications. However, this should not been seen in any way as limiting the scope of the described embodiments. The methods disclosed in this application are equally applicable to other communication media including optical and wireless communications. Thus, descriptive terms such as “voltage” or “signal level” should be considered to include equivalents in other measurement systems, such as “optical intensity”, “RF modulation”, etc. As used herein, the term “physical signal” includes any suitable behavior and/or attribute of a physical phenomenon capable of conveying information. Physical signals may be tangible and non-transitory.


Embodiments

In at least one embodiment, a method 800 comprises receiving, at step 802, a set of symbols of a codeword of a vector signaling code at a plurality of multi-input comparators (MICs), the set of symbols representing a transformation of an input vector with a non-simple orthogonal or unitary matrix, the input vector comprising a plurality of sub-channels, wherein at least one sub-channel corresponds to an input data signal and wherein at least one sub-channel corresponds to a data-aligned strobe signal, forming, at step 802 a set of MIC output signals based on a plurality of comparisons between a plurality of subsets of symbols of the codeword, wherein for each comparison, each subset of symbols has a set of input coefficients applied to it determined by a corresponding MIC, and wherein the set of MIC output signals comprises at least one data output signal and at least one received data-aligned strobe signal, and sampling, at step 806, the at least one data output signal according to the at least one received data-aligned strobe signal.


In at least one embodiment, at least one data output signal is sampled on a rising edge of at least one received data-aligned strobe signal. In another embodiment, at least one output data signal is sampled on a falling edge of at least one received data-aligned strobe signal.


In at least one embodiment, the input vector comprises 4 sub-channels corresponding to input data signals and 1 sub-channel corresponding to a data-aligned strobe signal. In at least one embodiment, each symbol of the set of symbols has a value selected from a set of at least two values. In a further embodiment, each symbol of the set of symbols has a value selected from the set of values {+1, +⅓, −⅓, −1}.


In at least one embodiment, the sets of input coefficients for each MIC are determined by the non-simple orthogonal or unitary matrix.


In at least one embodiment, the codeword is balanced.


In at least one embodiment, the method further comprises forming a set of output bits by slicing the set of MIC output signals.


In at least one embodiment, the method further comprises receiving the input vector on a plurality of wires, generating, using an encoder, the set of symbols of the codeword representing a weighted sum of sub-channel vectors, the sub-channel vectors corresponding to rows of the non-simple orthogonal or unitary matrix, wherein a weighting of each sub-channel vector is determined by a corresponding input vector sub-channel, and providing the symbols of the codeword on a multi-wire bus.


In at least one embodiment, an apparatus comprises a multi-wire bus configured to receive a set of symbols of a codeword of a vector signaling code, the set of symbols representing a transformation of an input vector with a non-simple orthogonal or unitary matrix, the input vector comprising a plurality of sub-channels, wherein at least one sub-channel corresponds to an input data signal and wherein at least one sub-channel corresponds to a data-aligned strobe signal, a plurality of multi-input comparators (MICs) configured to form a set of MIC output signals based on a plurality of comparisons between a plurality of subsets of symbols of the codeword, wherein for each comparison, each subset of symbols has a set of input coefficients applied to the subset determined by a corresponding MIC, and wherein the set of MIC output signals comprises at least one data output signal and at least one received data-aligned strobe signal, and a plurality of sampling circuits configured to sample the at least one data output signal according to the at least one received data-aligned strobe signal.


In at least one embodiment, at least one sampling circuit is configured to sample at least one data output signal on a rising edge of at least one received data-aligned strobe signal. In another embodiment, at least one sampling circuit is configured to sample at least one output data signal on a falling edge of at least one received data-aligned strobe signal.


In at least one embodiment, the input vector comprises 4 sub-channels corresponding to input data signals and 1 sub-channel corresponding to a data-aligned strobe signal. In at least one embodiment, each symbol of the set of symbols has a value selected from a set of at least two values. In a further embodiment, each symbol of the set of symbols has a value selected from the set of values {+1, +⅓, −⅓, −1}.


In at least one embodiment, the sets of input coefficients of each MIC are determined by the non-simple orthogonal or unitary matrix.


In at least one embodiment, the codeword is balanced.


In at least one embodiment, the apparatus further comprises a plurality of slicers configured to generate a set of output bits by slicing the set of MIC output signals.


In at least one embodiment, an apparatus comprises a plurality of wires configured to receive an input vector, the input vector comprising a plurality of sub-channels, wherein at least one sub-channel corresponds to a data signal, and wherein at least one sub-channel corresponds to a data-aligned strobe signal, an encoder configured to generate a set of symbols of a codeword representing a weighted sum of sub-channel vectors, the sub-channel vectors corresponding to rows of a non-simple orthogonal or unitary matrix, wherein a weighting of each sub-channel vector is determined by a corresponding input vector sub-channel, and a plurality of line drivers configured to transmit the symbols of the codeword on a multi-wire bus.

Claims
  • 1. A method comprising: obtaining a set of inputs comprising at least one input data signal and at least one clock signal, wherein the at least one clock signal is data-aligned to the at least one input data signal;generating symbols of a codeword of a balanced vector signaling code wherein all symbols of any given codeword sum to zero, the symbols representing a transformation of the set of inputs with a plurality of mutually orthogonal sub-channel vectors that collectively form an orthogonal matrix, each sub-channel vector weighted by a respective input of the set of inputs; andtransmitting each symbol of the codeword as an analog signal over a respective wire of a multi-wire bus.
  • 2. The method of claim 1, wherein the symbols of the codeword of the vector signaling code have symbol values selected from at least a ternary alphabet.
  • 3. The method of claim 2, wherein the at least ternary alphabet is a quaternary alphabet comprising a set of symbol values ±1, ±⅓.
  • 4. The method of claim 1, wherein the clock signal weights a sub-channel vector of the plurality of mutually orthogonal sub-channel vectors that affects all wires of the multi-wire bus.
  • 5. The method of claim 1, wherein the clock signal weights a sub-channel vector of the plurality of mutually orthogonal sub-channel vectors that affects two wires of the multi-wire bus.
  • 6. The method of claim 1, wherein the plurality of mutually orthogonal sub-channel vectors are distinct, orthogonal permutations of a vector [+1 +1 −1 −1].
  • 7. The method of claim 1, wherein the clock signal weights a sub-channel vector having equal magnitude elements.
  • 8. The method of claim 1, wherein the clock signal transitions no more than one time per unit interval.
  • 9. An apparatus comprising: an encoder configured to obtain a set of inputs comprising at least one input data signal and at least one clock signal, wherein the at least one clock signal is data-aligned to the at least one input data signal, and to responsively generate symbols of a codeword of a balanced vector signaling code wherein symbols of any given codeword sum to zero, the symbols representing a transformation of the set of inputs with a plurality of mutually orthogonal sub-channel vectors that collectively form an orthogonal matrix, each sub-channel vector weighted by a respective input of the set of inputs; anda plurality of drivers configured to transmit each symbol of the codeword as an analog signal over a respective wire of a multi-wire bus.
  • 10. The apparatus of claim 9, wherein the symbols of the codeword of the vector signaling code have symbol values selected from at least a ternary alphabet.
  • 11. The apparatus of claim 10, wherein the at least ternary alphabet is a quaternary alphabet comprising a set of symbol values ±1, ±⅓.
  • 12. The apparatus of claim 9, wherein the clock signal weights a sub-channel vector of the plurality of mutually orthogonal sub-channel vectors that affects all wires of the multi-wire bus.
  • 13. The apparatus of claim 9, wherein the clock signal weights a sub-channel vector of the plurality of mutually orthogonal sub-channel vectors that affects two wires of the multi-wire bus.
  • 14. The apparatus of claim 9, wherein the plurality of mutually orthogonal sub-channel vectors are distinct, orthogonal permutations of a vector [+1 +1 −1 −1].
  • 15. The apparatus of claim 9, wherein the clock signal weights a sub-channel vector having equal magnitude elements.
  • 16. The apparatus of claim 9, wherein the clock signal transitions no more than one time per unit interval.
CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No. 15/829,904, filed Dec. 2, 2017, entitled “Orthogonal Differential Vector Signaling Codes with Embedded Clock”, which is a continuation of U.S. application Ser. No. 15/285,316, filed Oct. 4, 2016, entitled “Orthogonal Differential Vector Signaling Codes with Embedded Clock”, which is a continuation of U.S. application Ser. No. 14/816,896, filed Aug. 3, 2015, entitled “Orthogonal Differential Vector Signaling Codes with Embedded Clock,” which claims priority to U.S. Provisional Patent Application 62/032,175, filed Aug. 1, 2014, entitled “Orthogonal Differential Vector Signaling Codes with Embedded Clock,” all of which are hereby incorporated herein by reference in their entirety for all purposes.

US Referenced Citations (220)
Number Name Date Kind
3196351 David Jul 1965 A
3970795 Allen Jul 1976 A
4163258 Ebihara et al. Jul 1979 A
4499550 Ray et al. Feb 1985 A
5053974 Penz Oct 1991 A
5166956 Baltus et al. Nov 1992 A
5311516 Kuznicki et al. May 1994 A
5331320 Cideciyan et al. Jul 1994 A
5412689 Chan et al. May 1995 A
5449895 Hecht et al. Sep 1995 A
5461379 Weinman Oct 1995 A
5511119 Lechleider Apr 1996 A
5553097 Dagher Sep 1996 A
5856935 Moy et al. Jan 1999 A
5982954 Delen et al. Nov 1999 A
6005895 Perino et al. Dec 1999 A
6084883 Norrell et al. Jul 2000 A
6084958 Blossom Jul 2000 A
6097732 Jung Aug 2000 A
6154498 Dabral et al. Nov 2000 A
6226330 Mansur May 2001 B1
6278740 Nordyke Aug 2001 B1
6317465 Akamatsu et al. Nov 2001 B1
6359931 Perino et al. Mar 2002 B1
6452420 Wong Sep 2002 B1
6483828 Balachandran et al. Nov 2002 B1
6504875 Perino et al. Jan 2003 B2
6556628 Poulton et al. Apr 2003 B1
6621427 Greenstreet Sep 2003 B2
6621945 Bissessur Sep 2003 B2
6650638 Walker et al. Nov 2003 B1
6661355 Cornelius et al. Dec 2003 B2
6766342 Kechriotis Jul 2004 B2
6865234 Agazzi Mar 2005 B1
6865236 Terry Mar 2005 B1
6876317 Sankaran Apr 2005 B2
6898724 Chang May 2005 B2
6927709 Kiehl Aug 2005 B2
6954492 Williams Oct 2005 B1
6990138 Bejjani et al. Jan 2006 B2
6999516 Rajan Feb 2006 B1
7023817 Kuffner et al. Apr 2006 B2
7039136 Olson et al. May 2006 B2
7053802 Cornelius May 2006 B2
7075996 Simon et al. Jul 2006 B2
7127003 Rajan et al. Oct 2006 B2
7142612 Horowitz et al. Nov 2006 B2
7167019 Broyde et al. Jan 2007 B2
7167523 Mansur Jan 2007 B2
7180949 Kleveland et al. Feb 2007 B2
7184483 Rajan Feb 2007 B2
7269212 Chau et al. Sep 2007 B1
7356213 Cunningham et al. Apr 2008 B1
7358869 Chiarulli et al. Apr 2008 B1
7400276 Sotiriadis et al. Jul 2008 B1
7535957 Ozawa et al. May 2009 B2
7583209 Duan Sep 2009 B1
7613234 Raghavan et al. Nov 2009 B2
7620116 Bessios et al. Nov 2009 B2
7633850 Ann Dec 2009 B2
7656321 Wang Feb 2010 B2
7706456 Laroia et al. Apr 2010 B2
7706524 Zerbe Apr 2010 B2
7746764 Rawlins et al. Jun 2010 B2
7841909 Murray et al. Nov 2010 B2
7868790 Bae Jan 2011 B2
7869546 Tsai Jan 2011 B2
7899653 Hollis Mar 2011 B2
8050332 Chung et al. Nov 2011 B2
8055095 Palotai et al. Nov 2011 B2
8064535 Wiley Nov 2011 B2
8085172 Li et al. Dec 2011 B2
8149906 Saito et al. Apr 2012 B2
8159375 Abbasfar Apr 2012 B2
8159376 Abbasfar Apr 2012 B2
8199849 Oh et al. Jun 2012 B2
8199863 Chen et al. Jun 2012 B2
8218670 Abou Jul 2012 B2
8245094 Jiang et al. Aug 2012 B2
8274311 Liu Sep 2012 B2
8279094 Abbasfar Oct 2012 B2
8279745 Dent Oct 2012 B2
8279976 Lin et al. Oct 2012 B2
8284848 Nam et al. Oct 2012 B2
8289914 Li et al. Oct 2012 B2
8295250 Gorokhov et al. Oct 2012 B2
8365035 Hara Jan 2013 B2
8442099 Sederat May 2013 B1
8442210 Zerbe May 2013 B2
8451913 Oh et al. May 2013 B2
8472513 Malipatil et al. Jun 2013 B2
8498344 Wilson et al. Jul 2013 B2
8498368 Husted et al. Jul 2013 B1
8520493 Goulahsen Aug 2013 B2
8539318 Shokrollahi et al. Sep 2013 B2
8577284 Seo et al. Nov 2013 B2
8588254 Diab et al. Nov 2013 B2
8588280 Oh et al. Nov 2013 B2
8593305 Tajalli et al. Nov 2013 B1
8620166 Guha Dec 2013 B2
8638241 Sudhakaran et al. Jan 2014 B2
8644497 Clausen et al. Feb 2014 B2
8649445 Cronie et al. Feb 2014 B2
8649460 Ware et al. Feb 2014 B2
8687968 Nosaka et al. Apr 2014 B2
8718184 Cronie May 2014 B1
8755426 Cronie Jun 2014 B1
8773964 Hsueh et al. Jul 2014 B2
8780687 Clausen et al. Jul 2014 B2
8831440 Yu et al. Sep 2014 B2
8879660 Peng et al. Nov 2014 B1
8938171 Tang et al. Jan 2015 B2
8949693 Ordentlich et al. Feb 2015 B2
8951072 Hashim et al. Feb 2015 B2
8989317 Holden Mar 2015 B1
8996740 Wiley et al. Mar 2015 B2
9015566 Cronie et al. Apr 2015 B2
9069995 Cronie Jun 2015 B1
9071476 Fox et al. Jun 2015 B2
9077386 Holden et al. Jul 2015 B1
9093791 Liang Jul 2015 B2
9100232 Hormati et al. Aug 2015 B1
9124557 Fox et al. Sep 2015 B2
9165615 Amirkhany et al. Oct 2015 B2
9197470 Okunev Nov 2015 B2
9231790 Wiley et al. Jan 2016 B2
9246713 Shokrollahi Jan 2016 B2
9251873 Fox et al. Feb 2016 B1
9288082 Ulrich et al. Mar 2016 B1
9288089 Cronie et al. Mar 2016 B2
9331962 Lida et al. May 2016 B2
9362974 Fox et al. Jun 2016 B2
9363114 Shokrollahi et al. Jun 2016 B2
9401828 Cronie et al. Jul 2016 B2
9432082 Ulrich et al. Aug 2016 B2
9455765 Schumacher et al. Sep 2016 B2
9461862 Holden et al. Oct 2016 B2
9479369 Shokrollahi Oct 2016 B1
9509437 Shokrollahi Nov 2016 B2
9537644 Jones et al. Jan 2017 B2
9634797 Benammar et al. Apr 2017 B2
9667379 Cronie et al. May 2017 B2
9710412 Sengoku Jul 2017 B2
10055372 Shokrollahi Aug 2018 B2
20010006538 Simon et al. Jul 2001 A1
20020044316 Myers Apr 2002 A1
20020152340 Dreps et al. Oct 2002 A1
20020174373 Chang Nov 2002 A1
20020181607 Izumi Dec 2002 A1
20030048210 Kiehl Mar 2003 A1
20030086366 Branlund et al. May 2003 A1
20030117184 Fecteau et al. Jun 2003 A1
20040057525 Rajan et al. Mar 2004 A1
20040146117 Subramaniam et al. Jul 2004 A1
20040155802 Lamy et al. Aug 2004 A1
20040161019 Raghavan et al. Aug 2004 A1
20040170231 Bessios et al. Sep 2004 A1
20040239374 Hori Dec 2004 A1
20050213686 Love et al. Sep 2005 A1
20060013331 Choi et al. Jan 2006 A1
20060018344 Pamarti Jan 2006 A1
20060126751 Bessios Jun 2006 A1
20060159005 Rawlins et al. Jul 2006 A1
20060291589 Eliezer et al. Dec 2006 A1
20070030796 Green Feb 2007 A1
20070164883 Furtner Jul 2007 A1
20070263711 Theodor et al. Nov 2007 A1
20080104374 Mohamed May 2008 A1
20080159448 Anim-Appiah et al. Jul 2008 A1
20080192621 Suehiro Aug 2008 A1
20080316070 Van et al. Dec 2008 A1
20090046009 Fujii Feb 2009 A1
20090059782 Cole Mar 2009 A1
20090154604 Lee et al. Jun 2009 A1
20100046644 Mazet Feb 2010 A1
20100054355 Kinjo et al. Mar 2010 A1
20100081451 Mueck et al. Apr 2010 A1
20100215112 Tsai et al. Aug 2010 A1
20100215118 Ware et al. Aug 2010 A1
20100235673 Abbasfar Sep 2010 A1
20100296556 Rave et al. Nov 2010 A1
20100309964 Oh et al. Dec 2010 A1
20110014865 Seo et al. Jan 2011 A1
20110084737 Oh et al. Apr 2011 A1
20110127990 Wilson et al. Jun 2011 A1
20110235501 Goulahsen Sep 2011 A1
20110268225 Cronie et al. Nov 2011 A1
20110286497 Nervig Nov 2011 A1
20110299555 Cronie et al. Dec 2011 A1
20110302478 Cronie et al. Dec 2011 A1
20120213299 Cronie et al. Aug 2012 A1
20130010892 Cronie Jan 2013 A1
20130013870 Cronie et al. Jan 2013 A1
20130114392 Sun et al. May 2013 A1
20130159584 Nygren et al. Jun 2013 A1
20130259113 Kumar Oct 2013 A1
20140112376 Wang et al. Apr 2014 A1
20140177645 Cronie et al. Jun 2014 A1
20140198837 Fox et al. Jul 2014 A1
20140226734 Fox Aug 2014 A1
20140254642 Fox et al. Sep 2014 A1
20140376604 Verlinden et al. Dec 2014 A1
20150063494 Simpson et al. Mar 2015 A1
20150078479 Whitby-Strevens Mar 2015 A1
20150092532 Shokrollahi et al. Apr 2015 A1
20150195005 De Lind Van Wijngaarden et al. Jul 2015 A1
20150222458 Hormati et al. Aug 2015 A1
20150236885 Ling et al. Aug 2015 A1
20150249559 Shokrollahi et al. Sep 2015 A1
20150333940 Shokrollahi Nov 2015 A1
20150349835 Fox et al. Dec 2015 A1
20150365263 Zhang et al. Dec 2015 A1
20150380087 Mittelholzer et al. Dec 2015 A1
20150381768 Fox et al. Dec 2015 A1
20160020824 Ulrich et al. Jan 2016 A1
20160036616 Holden et al. Feb 2016 A1
20160218894 Fox et al. Jul 2016 A1
20160380787 Hormati et al. Dec 2016 A1
20170272285 Shokrollahi et al. Sep 2017 A1
20190103903 Yang Apr 2019 A1
Foreign Referenced Citations (9)
Number Date Country
1864346 Nov 2006 CN
101854223 Oct 2010 CN
2039221 Feb 2013 EP
2003163612 Jun 2003 JP
2009084121 Jul 2009 WO
2010031824 Mar 2010 WO
2011119359 Sep 2011 WO
2011134678 Nov 2011 WO
2011151469 Dec 2011 WO
Non-Patent Literature Citations (20)
Entry
Abbasfar, Aliazam , “Generalized Differential Vector Signaling”, IEEE International Conference on Communications, ICC '09, Jun. 14, 2009, 1-5 (5 pages).
Anonymous , “Constant-weight code”, Wikipedia.org, retrieved on Feb. 6, 2017, (3 pages).
Cheng, Wei-Chung , et al., “Memory Bus Encoding for Low Power: A Tutorial”, Proceedings of the IEEE 2001. 2nd International Symposium on Quality Electronic Design, Mar. 28, 2001, 199-204 (6 pages).
Counts, Lew , et al., “One-Chip “Slide Rule” Works with Logs, Antilogs for Real-Time Processing”, Analog Devices, Computational Products 6, Reprinted from Electronic Design, May 2, 1985, 3-9 (7 pages).
Dasilva, Victor , et al., “Multicarrier Orthogonal CDMA Signals for Quasi-Synchronous Communication Systems”, IEEE Journal on Selected Areas in Communications, vol. 12, No. 5, Jun. 1994, 842-852 (11 pages).
Farzan, Kamran , et al., “Coding Schemes for Chip-to-Chip Interconnect Applications”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 14, No. 4, Apr. 2006, 393-406 (14 pages).
Giovaneli, Carlos Lopez, et al., “Space-Frequency Coded OFDM System for Multi-Wire Power Line Communications”, Power Line Communications and Its Applications, 2005 International Symposium on Vancouver, BC, Canada, IEEE XP-002433844, Apr. 6-8, 2005, 191-195 (5 pages).
Healey, Adam , et al., “A Comparison of 25 Gbps NRZ & PAM-4 Modulation used in Legacy & Premium Backplane Channels”, Tyco Electronics Corporation, DesignCon 2012, Jan. 2012, 1-16 (16 pages).
Holden, Brian , “An exploration of the technical feasibility of the major technology options for 400GE backplanes”, IEEE 802.3 400GE Study Group, Geneva, CH, Jul. 16, 2013, 1-18 (18 pages).
Holden, Brian , “Simulation results for NRZ, ENRZ & PAM-4 on 16-wire full-sized 400GE backplanes”, IEEE 802.3 400GE Study Group, York, UK, Sep. 2, 2013, 1-19 (19 pages).
Holden, Brian , “Using Ensemble NRZ Coding for 400GE Electrical Interfaces”, IEEE 802.3 400GE Study Group, May 17, 2013, 1-24 (24 pages).
Jiang, Anxiao , et al., “Rank Modulation for Flash Memories”, IEEE Transactions of Information Theory, vol. 55, No. 6, Jun. 2009, 2659-2673 (16 pages).
Oh, Dan , et al., “Pseudo-Differential Vector Signaling for Noise Reduction in Single-Ended Signaling Systems”, DesignCon 2009, Rambus Inc., Jan. 2009, (22 pages).
Poulton, John , “Multiwire Differential Signaling”, UNC-CH Department of Computer Science Version 1.1, Aug. 6, 2003, 1-20 (20 pages).
She, James , et al., “A Framework of Cross-Layer Superposition Coded Multicast for Robust IPTV Services over WiMAX”, IEEE Wireless Communications and Networking Conference, Apr. 15, 2008, 3139-3144 (6 pages).
Skliar, Osvaldo , et al., “A Method for the Analysis of Signals: the Square-Wave Method”, Revista de Matematica: Teoria y Aplicationes, vol. 15, No. 2, Mar. 2008, 109-129 (21 pages).
Slepian, David , “Permutation Modulation”, Proceedings of the IEE, vol. 53, No. 3, Mar. 1965, 228-236 (9 pages).
Stan, Mircea , et al., “Bus-Invert Coding for Low-Power I/O”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 3, No. 1, Mar. 1995, 49-58 (10 pages).
Tallini, Luca , et al., “Transmission Time Analysis for the Parallel Asynchronous Communication Scheme”, IEEE Transactions on Computers, vol. 52, No. 5,, May 2003, 558-571 (14 pages).
Wang, Xin , et al., “Applying CDMA Technique to Network-on-Chip”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 15, No. 10, Oct. 1, 2007, 1091-1100 (10 pages).
Related Publications (1)
Number Date Country
20190075004 A1 Mar 2019 US
Provisional Applications (1)
Number Date Country
62032175 Aug 2014 US
Continuations (3)
Number Date Country
Parent 15829904 Dec 2017 US
Child 16180953 US
Parent 15285316 Oct 2016 US
Child 15829904 US
Parent 14816896 Aug 2015 US
Child 15285316 US