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US-20260128750-A1 - DATA-DRIVEN NEURAL POLAR DECODER

US20260128750A1US 20260128750 A1US20260128750 A1US 20260128750A1US-20260128750-A1

Abstract

A method comprising: using a neural successive cancellation (NSC) polar codes decoder for communication or decompression, wherein the NSC polar codes decoder comprises the following Artificial Neural Networks (ANNs): (a) when the NSC polar codes decoder is used for communication: an output statistics ANN; (b) when the NSC polar codes decoder is used for decompression: an input statistics ANN; (c) a check-node ANN; (d) a bit-node ANN; and (e) a soft decision operations ANN.

Inventors

  • Bashar HULEIHEL
  • Ziv AHARONI
  • Haim Henry PERMUTER
  • Henry Pfister

Assignees

  • B. G. NEGEV TECHNOLOGIES AND APPLICATIONS LTD.
  • DUKE UNIVERSITY

Dates

Publication Date
20260507
Application Date
20240509

Claims (20)

  1. 1 . A method comprising: using a neural successive cancellation (NSC) polar codes decoder for communication or decompression, wherein the NSC polar codes decoder comprises the following Artificial Neural Networks (ANNs): (a) when the NSC polar codes decoder is used for communication: an output statistics ANN, (b) when the NSC polar codes decoder is used for decompression: an input statistics ANN, (c) a check-node ANN, (d) a bit-node ANN, and (e) a soft decision operations ANN.
  2. 2 . The method of claim 1 , wherein the NSC polar codes decoder is used for decompression, and wherein the method further comprises designing polar codes to compress data, the designing being based on the NSC polar codes decoder.
  3. 3 . The method of claim 2 , further comprising training the ANNs to decompress the compressed data.
  4. 4 . The method of claim 1 , wherein the NSC polar codes decoder is used for communication, and wherein the method further comprises designing polar codes to encode data to be transmitted over multiple communication channels, the designing being based on the NSC polar codes decoder.
  5. 5 . The method of claim 4 , further comprising training the ANNs to decode the data after the data have been received over the multiple communication channels.
  6. 6 . The method of claim 5 , wherein the training comprises determining parameters for the ANNs by estimating mutual information (MI) for each of the multiple communication channels.
  7. 7 . The method of claim 6 , wherein the designing of the polar codes comprises determining, using a Monte Carlo (MC) evaluation, which of the multiple communication channels are clean.
  8. 8 . The method of claim 5 , wherein the ANNs of (a), (c), (d), and (e) are trained jointly.
  9. 9 . The method of claim 6 , wherein the ANN of (a) is trained first, and the ANNs of (c), (d), and (e) are then trained while maintaining the determined parameters of the ANN of (a) fixed.
  10. 10 . The method of claim 4 , wherein a channel model of each of the multiple communication channels is unknown.
  11. 11 . The method of claim 4 , wherein: the multiple communication channels are communication channels with memory; and a computational complexity of the NSC polar codes decoder is not affected by the size of the memory.
  12. 12 . A system comprising: (i) at least one hardware processor; and (ii) a non-transitory computer-readable storage medium having program code embodied therewith, the program code executable by said at least one hardware processor to use a neural successive cancellation (NSC) polar codes decoder for communication or decompression, wherein the NSC polar codes decoder comprises the following Artificial Neural Networks (ANNs): (a) when the NSC polar codes decoder is used for communication: an output statistics ANN, (b) when the NSC polar codes decoder is used for decompression: an input statistics ANN, (c) a check-node ANN, (d) a bit-node ANN, and (e) a soft decision operations ANN.
  13. 13 . The system of claim 12 , wherein the NSC polar codes decoder is used for decompression, and wherein the program code is further executable to design polar codes to compress data, the designing being based on the NSC polar codes decoder.
  14. 14 . The system of claim 13 , wherein the program code is further executable to train the ANNs to decompress the compressed data.
  15. 15 . The system of claim 12 , wherein the NSC polar codes decoder is used for communication, and wherein the program code is further executable to design polar codes to encode data to be transmitted over multiple communication channels, the designing being based on the NSC polar codes decoder.
  16. 16 . The system of claim 15 , wherein the program code is further executable to train the ANNs to decode the data after the data have been received over the multiple communication channels.
  17. 17 . The system of claim 16 , wherein the training comprises determining parameters for the ANNs by estimating mutual information (MI) for each of the multiple communication channels.
  18. 18 . The system of claim 17 , wherein the designing of the polar codes comprises determining, using a Monte Carlo (MC) evaluation, which of the multiple communication channels are clean.
  19. 19 . The system of claim 16 , wherein the ANNs of (a), (c), (d), and (e) are trained jointly.
  20. 20 . The system of claim 17 , wherein the ANN of (a) is trained first, and the ANNs of (c), (d), and (e) are then trained while maintaining the determined parameters of the ANN of (a) fixed.

Description

CROSS-REFERENCE TO RELATED APPLICATION This application claims priority to U.S. Provisional Patent Application No. 63/465,258, filed May 10, 2023, entitled “Data Driven Polar Codes,” the contents of which are incorporated herein by reference in their entirety. FIELD The invention relates to the field of error detection and correction (EDAC), and more specifically to polar codes. BACKGROUND Polar codes are a type of error-correction codes introduced by Erdal Arikan in “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels,” IEEE Transactions on Information Theory, 55(7):3051-3073, 2009. Throughout this disclosure, any reference to Arikan is to his aforementioned paper, unless explicitly mentioned otherwise. Polar codes allow the construction of capacity-achieving codes for symmetric binary-input, discrete, memoryless channels (B-DMCs). When given N independent copies of a B-DMC W, successive cancellation (SC) decoding induces a new set of N binary-input synthesized (virtual) channels WN(i). Channel polarization is the phenomenon identified by Arikan, whereby, for N sufficiently large, almost all of the synthesized channels WN(i) have capacities close to 0 or 1. Specifically, the fraction of channels with capacity close to 1 approaches I(W) and the fraction of channels with capacity close to 0 approaches 1−I(W), where I(W) is the channel's symmetric capacity. The construction of polar codes involves choosing which rows to keep from the square generator matrix given by Arikan's transform, such that the polar codes ultimately allocate data bits to the most reliable, clean channels—those whose capacity approaches 1. The encoding and decoding procedures are performed by recursive formulas whose computational complexity is O(N log N). Polar codes can also be applied to finite state channels (FSCs). Arikan's transform also polarizes the bit channels WN(i) in the presence of memory (see E. Sasoglu and I. Tal, “Polar Coding for Processes with Memory,” IEEE Trans. Inf. Theory, vol. 65, no. 4, pp. 1994-2003, 2019; and B. Shuval and I. Tal, “Fast Polarization for Processes with Memory,” IEEE Trans. Inf. Theory, vol. 65, no. 4, pp. 2004-2020, 2018), and thus the encoding algorithm is the same as if the channel is memoryless. However, the decoding algorithm needs to be updated since the derivation of the SC decoder in Arikan relies on the memoryless property. To account for the channel memory, the channel outputs are represented by a trellis, whose nodes capture the information of the channel's memory. This trellis was embedded into the SC decoding algorithm to yield the SCT decoding algorithm (see R. Liu and Y. Hou, “Joint Successive Cancellation Decoding of Polar Codes Over Intersymbol Interference Channels,” arXiv:1404.3001, 2014; and R. Wang, J. Honda, H. Yamamoto, R. Liu, and Y. Hou, “Construction of polar codes for channels with memory,” 2015 IEEE Information Theory Workshop—Fall, IEEE, pp. 187-191, 2015). However, the SCT decoder is only applicable when the channel model is known and when the channel's state alphabet size is finite and relatively small. For FSCs the computational complexity of the SCT decoder is O(||3N log N), where || is the number of channel states. For Markov channels where the set of channel states is not finite, the SCT decoder is not applicable without quantization of its states. With quantization, there may be a strong tension between the computational complexity and the error introduced by quantization. Additionally, the SCT decoder cannot be used for an unknown channel with memory without first estimating the channel, as it requires an explicit channel model. The SCT decoder can also be applied to a larger class of channels (e.g., insertion and deletion channels) where, given the channel output sequence YN, a trellis can be constructed to efficiently represent PXN,YN (see I. Tal, H. D. Pfister, A. Fazeli, and A. Vardy, “Polar Codes for the Deletion Channel: Weak and Strong Polarization,” IEEE Trans. Inf. Theory, vol. 68, no. 4 pp 2239-2265, 2021). In that case, the decoding complexity is upper bounded by O(||3N log N), where |S| is the maximum number of states in any trellis stage. If ||grows linearly with N, then the complexity of the decoder may grow very rapidly (e.g., ≥N4) and is dominated by the number of trellis states rather than the block length. Today, most notably, polar codes are used for certain aspects of channel coding in 3GPP's fifth-generation (5G) cellular communications standard, and are embedded in various 5G network appliances, such as base stations and end-user devices. Polar codes remain attractive for various other technologies as well. The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the f