A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes

TL;DR

This paper investigates how locality in binary cyclic codes influences decoding performance, demonstrating improvements in signal-to-noise ratio, reduced state complexity, and faster decoding speeds through modified decoding strategies and code structure insights.

Contribution

It introduces modifications to ordered statistics decoding and trellis decoding that leverage locality, leading to enhanced decoding efficiency and lower complexity for binary cyclic codes.

Findings

OSD gains in SNR with locality modifications

Lower maximum state complexity in trellis decoding due to locality

Decoding speed increases significantly at high SNR with quick-look decoder

Abstract

In this paper, we study the impact of locality on the decoding of binary cyclic codes under two approaches, namely ordered statistics decoding (OSD) and trellis decoding. Given a binary cyclic code having locality or availability, we suitably modify the OSD to obtain gains in terms of the Signal-To-Noise ratio, for a given reliability and essentially the same level of decoder complexity. With regard to trellis decoding, we show that careful introduction of locality results in the creation of cyclic subcodes having lower maximum state complexity. We also present a simple upper-bounding technique on the state complexity profile, based on the zeros of the code. Finally, it is shown how the decoding speed can be significantly increased in the presence of locality, in the moderate-to-high SNR regime, by making use of a quick-look decoder that often returns the ML codeword.