Design of LDPC Code Ensembles with Fast Convergence Properties

TL;DR

This paper presents a method for designing LDPC code ensembles optimized for a specific finite number of decoder iterations, using EXIT chart analysis and differential evolution, to improve performance in practical decoding scenarios.

Contribution

It introduces a novel design approach for LDPC codes tailored to a fixed number of iterations, including generalized LDPC codes, demonstrating improved performance over traditional methods.

Findings

Codes optimized for a specific iteration count outperform others in that regime.

Generalized LDPC codes can outperform standard LDPC codes for low-iteration decoding.

Optimized codes show distinct degree distributions and weight enumerators compared to conventional designs.

Abstract

The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary erasure channel and additive white Gaussian noise channel. The error rates of codes optimized for various numbers of decoder iterations are compared and it is seen that in the cases considered, the best performance for a given number of decoder iterations is achieved by codes which are optimized for this particular number. The design of generalized LDPC (GLDPC) codes is also considered, showing that these structures can offer better performance than LDPC codes for low-iteration-number designs. Finally, it is illustrated that LDPC codes which are optimized for a small number of iterations exhibit significant deviations in terms of degree distribution and weight enumerators with respect to LDPC codes returned by more conventional design tools.