Optimization-Based Decoding Algorithms for LDPC Convolutional Codes in Communication Systems

TL;DR

This paper introduces optimization-based decoding algorithms for LDPC convolutional codes, focusing on integer programming techniques that improve decoding speed and accuracy over traditional heuristics in noisy communication channels.

Contribution

The paper presents novel integer programming-based exact and heuristic decoding algorithms for LDPC convolutional codes, including relax-and-fix heuristics that operate in small windows.

Findings

Near-optimal solutions achieved faster than commercial solvers at high error rates

Higher quality solutions compared to standard iterative heuristics

Decoding algorithms are effective for long information sequences in streaming applications

Abstract

In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information by adding redundant bits. Low-density parity-check (LDPC) convolutional codes, a member of the LDPC code family, encode the original information to improve error correction capability. In practice these codes are used to decode very long information sequences, where the information arrives in subsequent packets over time, such as video streams. We consider the problem of decoding the received information with minimum error from an optimization point of view and investigate integer programming-based exact and heuristic decoding algorithms for its solution. In particular, we consider relax-and-fix heuristics that decode information in small windows. Computational results indicate that our approaches identify near-optimal solutions significantly faster than a commercial solver in high channel error rates. Our proposed algorithms can find higher quality solutions compared with commonly used iterative decoding heuristics.