Low-Complexity Decoding for Low-Rate Block Codes of Short Length Based on Concatenated Coding Structure

TL;DR

This paper introduces a concatenated coding-based decoding method that improves reliability and reduces complexity for short, low-rate block codes by refining the most reliable position frame using LLRs from an inner code.

Contribution

It proposes an enhanced MRIP frame based on concatenated coding and LLRs, enabling more efficient decoding of short low-rate block codes compared to traditional methods.

Findings

Constructed concatenated codes outperform the (128,36) eBCH code in efficiency.

The method reduces decoding complexity while maintaining near-optimal performance.

Demonstrated effectiveness on various length-128 codes.

Abstract

To decode a short linear block code, ordered statics decoding (OSD) and/or the $A^*$ decoding are usually considered. Either OSD or the $A^*$ decoding utilizes the magnitudes of the received symbols to establish the most reliable and independent positions (MRIP) frame. A restricted searched space can be employed to achieve near-optimum decoding with reduced decoding complexity. For a low-rate code with large minimum distance, the restricted search space is still very huge. We propose to use concatenated coding to further restrict the search space by proposing an improved MRIP frame. The improved MRIP frame is founded according to magnitudes of log likelihood ratios (LLRs) obtained by the soft-in soft-out (SISO) decoder for the inner code. We focus on the construction and decoding of several $(n,k)$ = (128,36) binary linear block codes based on concatenated coding. We use the (128,36) extended BCH (eBCH) code as a benchmark for comparison. Simulation shows that there exist constructed concatenated codes which are much more efficient than the (128,36) eBCH code. Some other codes of length 128 or close to 128 are also constructed to demonstrate the efficiency of the proposed scheme.