Protograph LDPC Codes with Block Thresholds: Extension to Degree-1 and Generalized Nodes

TL;DR

This paper extends the design of protograph LDPC codes to include degree-1 and generalized nodes, providing conditions for threshold equality and demonstrating improved error performance near capacity.

Contribution

It introduces new conditions for threshold equality in protograph LDPC codes with degree-1 and generalized nodes, enabling near-capacity low-rate code design.

Findings

Codes with block-error thresholds close to capacity

Better error rate performance than existing codes

Conditions for threshold equality in generalized protographs

Abstract

Protograph low-density-parity-check (LDPC) are considered to design near-capacity low-rate codes over the binary erasure channel (BEC) and binary additive white Gaussian noise (BIAWGN) channel. For protographs with degree-one variable nodes and doubly-generalized LDPC (DGLDPC) codes, conditions are derived to ensure equality of bit-error threshold and block-error threshold. Using this condition, low-rate codes with block-error threshold close to capacity are designed and shown to have better error rate performance than other existing codes.