Successive Cancellation List Decoding of Product Codes with Reed-Muller Component Codes

TL;DR

This paper introduces successive cancellation list decoding for product codes with Reed-Muller components, demonstrating improved performance over belief propagation in short codes and concatenated configurations.

Contribution

It presents a novel SCL decoding approach for product codes with RM components, leveraging a Hadamard kernel interpretation, and shows performance gains over BP decoding.

Findings

SCL decoding with moderate list size matches or exceeds BP decoding for short codes.

Concatenating with a high-rate outer code enhances SCL decoding performance.

SCL decoding can outperform BP decoding by up to 1.4 dB in certain configurations.

Abstract

This letter proposes successive cancellation list (SCL) decoding of product codes with Reed--Muller (RM) component codes. SCL decoding relies on a product code description based on the $2\times 2$ Hadamard kernel, which enables interpreting the code as an RM subcode. The focus is on a class of product codes considered in wireless communication systems, based on single parity-check and extended Hamming component codes. For short product codes, it is shown that SCL decoding with a moderate list size performs as well as (and, sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by concatenating a short product code with a high-rate outer code, SCL decoding outperforms BP decoding by up to $1.4$ dB.