An Iterative Joint Linear-Programming Decoding of LDPC Codes and Finite-State Channels

TL;DR

This paper presents an efficient iterative joint LP decoding algorithm for LDPC codes over finite-state channels, combining the predictability of LP decoding with the performance of turbo equalization.

Contribution

It extends iterative approximate LP decoding to joint decoding of LDPC codes and FSCs, offering a convergent algorithm with complexity similar to turbo equalization.

Findings

Achieves joint decoding with LP-like performance

Complexity comparable to turbo equalization

Demonstrates improved decoding predictability

Abstract

In this paper, we introduce an efficient iterative solver for the joint linear-programming (LP) decoding of low-density parity-check (LDPC) codes and finite-state channels (FSCs). In particular, we extend the approach of iterative approximate LP decoding, proposed by Vontobel and Koetter and explored by Burshtein, to this problem. By taking advantage of the dual-domain structure of the joint decoding LP, we obtain a convergent iterative algorithm for joint LP decoding whose structure is similar to BCJR-based turbo equalization (TE). The result is a joint iterative decoder whose complexity is similar to TE but whose performance is similar to joint LP decoding. The main advantage of this decoder is that it appears to provide the predictability of joint LP decoding and superior performance with the computational complexity of TE.