Performance versus Complexity Per Iteration for Low-Density Parity-Check Codes: An Information-Theoretic Approach

TL;DR

This paper investigates the tradeoff between decoding performance and complexity per iteration for LDPC codes using information-theoretic bounds, providing insights into the sub-optimality of message-passing algorithms and improving existing bounds.

Contribution

It generalizes information-theoretic bounds for LDPC codes to parallel channels and punctured ensembles, enhancing the understanding of performance-complexity tradeoffs.

Findings

Bounds indicate sub-optimality of message-passing decoding

Generalized bounds for punctured LDPC codes and parallel channels

Improved tightness of existing information-theoretic bounds

Abstract

The paper is focused on the tradeoff between performance and decoding complexity per iteration for LDPC codes in terms of their gap (in rate) to capacity. The study of this tradeoff is done via information-theoretic bounds which also enable to get an indication on the sub-optimality of message-passing iterative decoding algorithms (as compared to optimal ML decoding). The bounds are generalized for parallel channels, and are applied to ensembles of punctured LDPC codes where both intentional and random puncturing are addressed. This work suggests an improvement in the tightness of some information-theoretic bounds which were previously derived by Burshtein et al. and by Sason and Urbanke.