Pruning Neural Belief Propagation Decoders

Abstract

We consider near maximum-likelihood (ML) decoding of short linear block codes. In particular, we propose a novel decoding approach based on neural belief propagation (NBP) decoding recently introduced by Nachmani et al. in which we allow a different parity-check matrix in each iteration of the algorithm. The key idea is to consider NBP decoding over an overcomplete parity-check matrix and use the weights of NBP as a measure of the importance of the check nodes (CNs) to decoding. The unimportant CNs are then pruned. In contrast to NBP, which performs decoding on a given fixed parity-check matrix, the proposed pruning-based neural belief propagation (PB-NBP) typically results in a different paritycheck matrix in each iteration. For a given complexity in terms of CN evaluations, we show that PB-NBP yields significant performance improvements with respect to NBP. We apply the proposed decoder to the decoding of a Reed-Muller code, a short low-density parity-check (LDPC) code, and a polar code. PB-NBP outperforms NBP decoding over an overcomplete paritycheck matrix by 0.27-0.31 dB while reducing the number of required CN evaluations by up to 97%. For the LDPC code, PB-NBP outperforms conventional belief propagation with the same number of CN evaluations by 0.52 dB. We further extend the pruning concept to offset min-sum decoding and introduce a pruning-based neural offset min-sum (PB-NOMS) decoder, for which we jointly optimize the offsets and the quantization of the messages and offsets. We demonstrate performance 0.5 dB from ML decoding with 5-bit quantization for the Reed-Muller code.

Towards Practical Near-Maximum-Likelihood Decoding of Error-Correcting Codes: An Overview

“…The error probability of the decoders proposed in [29] is within 0.27 dB and 1.5 dB of the ML performance, while significantly reducing the decoding complexity. In [30] the authors extend the work in [29] to further improve the error probability of neural BP decoders.…”

“…It was shown in [28] that the trainable parameters can be optimized using supervised learning techniques to greatly improve the error-correction performance of the code. In [29], the authors proposed a technique to efficiently prune the unimportant edges of the unrolled factor graph of a linear block code at each decoding iteration. The error probability of the decoders proposed in [29] is within 0.27 dB and 1.5 dB of the ML performance, while significantly reducing the decoding complexity.…”

“…In [29], the authors proposed a technique to efficiently prune the unimportant edges of the unrolled factor graph of a linear block code at each decoding iteration. The error probability of the decoders proposed in [29] is within 0.27 dB and 1.5 dB of the ML performance, while significantly reducing the decoding complexity. In [30] the authors extend the work in [29] to further improve the error probability of neural BP decoders.…”

Learned Decimation for Neural Belief Propagation Decoders : Invited Paper

“…of pruning-based NBP D 3 in[10]. Adding a single learned decimation (NBP-D(10, 4, 1)) improves the performance by 0.3 dB.…”

“…Adding a single learned decimation (NBP-D(10, 4, 1)) improves the performance by 0.3 dB. Allowing four learned decimation steps (NBP-D(10,4,4)…”