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arXiv:2210.16227

Recursive/Iterative unique Projection-Aggregation of RM codes

Marzieh Hashemipour-Nazari, Renate Debets, Kees G. W. Goossens, Alexios Balatsoukas‐Stimming

Published Oct 28, 2022• 0 citations
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Abstract

We describe recursive unique projection-aggregation (RUPA) decoding and iterative unique projection-aggregation (IUPA) decoding of Reed-Muller (RM) codes, which remove non-unique projections from the recursive projection-aggregation (RPA) and iterative projection-aggregation (IPA) algorithms respectively. We show that these algorithms have competitive error-correcting performance while requiring up to 95% projections less than the baseline RPA algorithm.

DOI
10.48550/arxiv.2210.16227

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The recently proposed recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller codes has received significant attention as it provides near-ML decoding performance at reasonable complexity for short codes. However, its complicated structure makes it unsuitable for hardware implementation. Iterative projection-aggregation (IPA) decoding is a modified version of RPA decoding that simplifies the hardware implementation. In this work, we present a flexible hardware architecture for the IPA decoder that can be configured from fully-sequential to fully-parallel, thus making it suitable for a wide range of applications with different constraints and resource budgets. Our simulation and implementation results show that the IPA decoder has 41% lower area consumption, 44% lower latency, four times higher throughput, but currently seven times higher power consumption for a code with block length of 128 and information length of 29 compared to a state-of-the-art polar successive cancellation list (SCL) decoder with comparable decoding performance.
The recursive projection-aggregation (RPA) decoding algorithm for Reed-Muller (RM) codes was recently introduced by Ye and Abbe. We show that the RPA algorithm is closely related to (weighted) belief-propagation (BP) decoding by interpreting it as a message-passing algorithm on a factor graph with redundant code constraints. We use this observation to introduce a novel decoder tailored to high-rate RM codes. The new algorithm relies on puncturing rather than projections and is called recursive puncturing-aggregation (RXA). We also investigate collapsed (i.e., non-recursive) versions of RPA and RXA and show some examples where they achieve similar performance with lower decoding complexity.
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.