Low-Complexity Decoding of a Class of Reed-Muller Subcodes for Low-Capacity Channels

TL;DR

This paper introduces a low-complexity, low-latency iterative decoding algorithm for a class of Reed-Muller subcodes, optimized for low-capacity channels, with significant improvements in efficiency and performance over traditional methods.

Contribution

It proposes a novel multi-dimensional product code construction and an efficient SISO iterative decoding algorithm for Reed-Muller subcodes, reducing complexity and latency.

Findings

Decoding complexity is $ ext{O}(n ext{log} n)$

Latency is $ ext{O}( ext{log} n)$

Superiority over hard decoding methods demonstrated

Abstract

We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array, and the encoding over each dimension is done separately via a smaller RM encoder. Similarly, the decoding is performed over each dimension via a low-complexity decoder for smaller RM codes. The proposed construction is of particular interest to low-capacity channels that are relevant to emerging low-rate communication scenarios. We present an efficient soft-input soft-output (SISO) iterative decoding algorithm for the product of RM codes and demonstrate its superiority compared to hard decoding over RM code components. The proposed coding scheme has decoding (as well as encoding) complexity of $\mathcal{O}(n\log n)$ and latency of $\mathcal{O}(\log n)$ for blocklength $n$. This research renders a general framework toward efficient decoding of RM codes.