Soft Decision Decoding of Recursive Plotkin Constructions Based on Hidden Code Words

TL;DR

This paper introduces novel soft-decision decoding algorithms for recursive Plotkin constructions, exploiting hidden code words to approach maximum-likelihood performance with low complexity, applicable to Reed-Muller and generalized concatenated codes.

Contribution

The paper presents new soft-decision decoders based on hidden code words in recursive Plotkin constructions, achieving near-ML performance with low complexity.

Findings

Decoding variants improve performance closer to ML bounds.

Decoders use only simple operations like additions and sign checks.

Introduces two new classes of half-rate codes based on recursive Plotkin structures.

Abstract

The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be described as recursive Plotkin construction. Exploiting a property of the code words constructed by the recursive Plotkin construction, we present novel soft-decision decoders. These are based on the decoding of hidden code words which are inherent contained in the constructed code words and can be uncovered by adding particular parts of the overall code word. The main idea is to use more than one decoding variant where each variant starts with the decoding of a different hidden code word. The final decoding decision selects the best of the decisions of the used variants. The more variants are used the closer the performance gets to the maximum-likelihood (ML) decoding performance. This is verified by an ML-bound for the cases where the ML performance is not known. The decoding algorithms use only additions, comparisons, and sign operations. Further, due to the recursive structure, only relatively short codes have to be decoded, thus, the decoding complexity is very low. In addition, we introduce two novel classes of half-rate codes based on recursive Plotkin constructions with RM codes.