Generalized LDPC codes with low-complexity decoding and fast convergence

TL;DR

This paper introduces generalized LDPC codes with novel low-complexity decoding algorithms, demonstrating improved convergence and performance over 5G LDPC codes, especially at fewer iterations.

Contribution

It proposes two efficient decoding algorithms for GLDPC codes based on latent variables and message passing, with optimized code design for fast convergence.

Findings

Comparable performance to 5G LDPC at 50 iterations

Significantly better convergence at 10 iterations

Effective optimization using density evolution

Abstract

We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product decoding, and another based on evaluating two hypotheses per bit, referred to as the Min-Sum decoder. Both algorithms are derived using latent variables and an appropriate message-passing schedule. A quantized, protograph-based density evolution procedure is used to optimize GLDPC codes for Min-Sum decoding. Compared to 5G LDPC codes, the proposed GLDPC codes offer similar performance at 50 iterations and significantly better convergence and performance at 10 iterations.