Deriving Good LDPC Convolutional Codes from LDPC Block Codes

TL;DR

This paper presents graph-cover-based methods to derive LDPC convolutional codes from block codes, demonstrating significant performance improvements and analyzing the reasons behind the convolutional gain.

Contribution

It introduces a unified framework for constructing LDPC convolutional codes from block codes, including existing methods, and analyzes their performance benefits.

Findings

Some convolutional codes outperform their block code counterparts.

Convolutional gain is attributed to specific structural advantages.

Moderate increase in decoder complexity is observed.

Abstract

Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework. Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this "convolutional gain," and we also discuss the --- mostly moderate --- decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.