Approaching Blokh-Zyablov Error Exponent with Linear-Time Encodable/Decodable Codes

TL;DR

This paper demonstrates that Blokh-Zyablov error exponents can be approached with linear-time encodable and decodable codes over general channels, extending previous results from binary symmetric channels.

Contribution

It introduces a revised decoding algorithm that integrates Guruswami-Indyk's outer codes into concatenated schemes with linear complexity, applicable to general discrete channels.

Findings

Achieves Forney's and Blokh-Zyablov error exponents with linear complexity

Extends results from binary symmetric channels to general discrete channels

Provides a revised decoding algorithm for concatenated codes

Abstract

Guruswami and Indyk showed in [1] that Forney's error exponent can be achieved with linear coding complexity over binary symmetric channels. This paper extends this conclusion to general discrete-time memoryless channels and shows that Forney's and Blokh-Zyablov error exponents can be arbitrarily approached by one-level and multi-level concatenated codes with linear encoding/decoding complexity. The key result is a revision to Forney's general minimum distance decoding algorithm, which enables a low complexity integration of Guruswami-Indyk's outer codes into the concatenated coding schemes.