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arXiv:2011.12882 · IEEE International Symposium on Information Theory (ISIT)

Sparse Multi-Decoder Recursive Projection Aggregation for Reed-Muller Codes

Dorsa Fathollahi, Nariman Farsad, Seyyed Ali Hashemi, Marco Mondelli

Published Jul 12, 2021• 30 citations
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Abstract

Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoder's computations by up to 80% with negligible performance loss.

DOI
10.1109/isit45174.2021.9517887

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Reed-Muller (RM) codes are one of the oldest families of codes. Recently, a recursive projection aggregation (RPA) decoder has been proposed, which achieves a performance that is close to the maximum likelihood decoder for short-length RM codes. One of its main drawbacks, however, is the large amount of computations needed. In this paper, we devise a new algorithm to lower the computational budget while keeping a performance close to that of the RPA decoder. The proposed approach consists of multiple sparse RPAs that are generated by performing only a selection of projections in each sparsified decoder. In the end, a cyclic redundancy check (CRC) is used to decide between output codewords. Simulation results show that our proposed approach reduces the RPA decoder's computations by up to 80% with negligible performance loss.
Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called sparse multi-decoder RPA (SRPA), has been proposed [2]. The SRPA approach makes use of multiple pruned RPA decoders to lower the amount of computations while keeping the performance loss small compared to RPA decoding. However, the use of multiple sparse decoders again increases the computational burden. Therefore, the focus is on the optimization of sparse single-decoder RPA decoding to keep the complexity small. In this paper, a novel method is proposed, to select subsets of subspaces used in the projection and aggregation step of SRPA decoding in order to decrease the decoding error probability on AWGN channels. The proposed method replaces the random selection of subspace subsets with a semi-deterministic selection method based on a figure of merit that evaluates the performance of each subspace. Our simulation results show that the semi-deterministic subspace selection improves the decoding performance up to 0.2 dB0.2\,\text{dB}0.2dB compared to SRPA. At the same time, the complexity of SRPA decoding for RM codes of order r≥3r\geq 3r≥3 is reduced by up to 81% compared to SRPA.
The recursive projection-aggregation (RPA) decoder is a recently proposed near maximum likelihood (ML) decoder for Reed-Muller (RM) codes with low rates and short code lengths. However, the high computational complexity of RPA decoding is a major bottleneck for using RPA in applications that have a limited resource and energy budget. In this work, syndrome-based early stopping techniques as well as a scheduling scheme are proposed for the RPA decoder, which help in reducing the computational complexity while keeping similar decoding performance. Comparing to the baseline RPA decoder, the proposed techniques result in a 69−98% reduction in the average computational complexity for a target frame error rate (FER) of 10−5. Additionally, this work introduces hardware-friendly approximation functions to replace the RPA’s computationally expensive transcendental projection function.
The recently introduced recursive projection aggregation (RPA) decoding method for Reed-Muller (RM) codes can achieve near-maximum likelihood (ML) decoding performance. However, its high computational complexity makes its implementation challenging for time- and resource-critical applications. In this work, we present a complexity reduction technique called multi-factor pruning that reduces the computational complexity of RPA significantly. Our simulation results show that the proposed pruning approach with appropriately selected factors can reduce the complexity of RPA by up to 92% for RM(8, 3) while keeping a comparable error-correcting performance.
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) regime for a wide range of code rates. Simulation results show that in both low code rate and high code rate regimes, the new algorithm outperforms the widely used decoder for polar codes (SCL+CRC) with the same parameters. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms based on list-decoding algorithms and code concatenation. We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.
We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤1024\le 1024≤1024) regime for a wide range of code rates. Simulation results show that in both low code rate and high code rate regimes, the new algorithm outperforms the widely used decoder for polar codes (SCL+CRC) with the same parameters. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.