Protograph-Based Low-Density Parity-Check Hadamard Codes

TL;DR

This paper introduces a novel design for LDPC-Hadamard codes using protograph constraints, achieving near-Shannon-limit performance with optimized thresholds and error rates, and extends analysis to punctured codes.

Contribution

The paper presents a new protograph-based design method for LDPC-Hadamard codes and a modified PEXIT algorithm for analysis and optimization.

Findings

Decoding thresholds range from -1.53 dB to -1.42 dB.

Gaps to Shannon limit are between 0.16 dB and 0.40 dB.

Error performance is comparable to traditional LDPC-Hadamard codes.

Abstract

In this paper, we propose a new method to design low-density parity-check Hadamard (LDPC-Hadamard) codes, a type of ultimate-Shannon-limit approaching channel codes. The technique is based on applying Hadamard constraints to the check nodes in a generalized protograph-based LDPC code, followed by lifting the generalized protograph. We name the codes formed protograph-based LDPC Hadamard (PLDPC-Hadamard) codes. We also propose a modified Protograph Extrinsic Information Transfer (PEXIT) algorithm for analyzing and optimizing PLDPC-Hadamard code designs. The proposed algorithm further allows the analysis of PLDPC-Hadamard codes with degree-1 and/or punctured nodes. We find codes with decoding thresholds ranging from -1.53 dB to -1.42 dB. At a BER of 1e-5, the gaps of our codes to the ultimate-Shannon-limit range from 0.40 dB (for rate = 0.0494) to 0.16 dB (for rate = 0.003). Moreover, the error performance of our codes is comparable to that of the traditional LDPC-Hadamard codes. Finally, the BER performances of our codes after puncturing are simulated and compared.