TY - JOUR
T1 - Protograph-Based LDPC Hadamard Codes
AU - Zhang, Peng Wei
AU - Lau, Francis C.M.
AU - Sham, Chiu Wing
N1 - Funding Information:
Manuscript received September 29, 2020; revised January 6, 2021 and March 27, 2021; accepted April 28, 2021. Date of publication May 6, 2021; date of current version August 16, 2021. The work described in this paper was supported by a grant from the RGC of the Hong Kong SAR, China (Project No. PolyU 152170/18E). This article was presented in part at WCNC 2020 [1]. The associate editor coordinating the review of this article and approving it for publication was J. Yuan. (Corresponding author: Francis C. M. Lau.) Peng-Wei Zhang and Francis C. M. Lau are with the Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Hong Kong (e-mail: [email protected]; [email protected]).
Publisher Copyright:
© 1972-2012 IEEE.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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.
KW - PEXIT algorithm
KW - PLDPC-Hadamard code
KW - Protograph LDPC code
KW - ultimate Shannon limit
UR - http://www.scopus.com/inward/record.url?scp=85105865553&partnerID=8YFLogxK
U2 - 10.1109/TCOMM.2021.3077939
DO - 10.1109/TCOMM.2021.3077939
M3 - Journal article
AN - SCOPUS:85105865553
SN - 0090-6778
VL - 69
SP - 4998
EP - 5013
JO - IEEE Transactions on Communications
JF - IEEE Transactions on Communications
IS - 8
M1 - 9424609
ER -