Protograph-Based LDPC Hadamard Codes

Peng Wei Zhang, Francis C.M. Lau, Chiu Wing Sham

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


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 10-5, 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.

Original languageEnglish
Article number9424609
Pages (from-to)4998-5013
Number of pages16
JournalIEEE Transactions on Communications
Issue number8
Publication statusPublished - Aug 2021


  • PEXIT algorithm
  • PLDPC-Hadamard code
  • Protograph LDPC code
  • ultimate Shannon limit

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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