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International Joint Conference on Information and Communication Engineering (JCICE)

Optimization of Root-Protograph LDPC Codes for Joint Source Channel Coding System over Block Fading Channel

Jihua Wu, Mengyao Wang, Qiwang Chen, Chen Chen

Published May 1, 2023• 1 citation
Publisher

Abstract

Double protograph low-density parity-check (DP-LDPC) codes based on the joint source channel coding (JSCC) system has been demonstrated to have outstanding error performance over additive white Gaussian noise (AWGN) channels. However, because of the non-ergodic nature of the block-fading (BF) channels, the protograph low-density parity-check (PLDPC) codes cannot perform well over BF channel. Whereby the excellent error performance of root protograph LDPC (RPLDPC) codes under BF channel, we utilize RPLDPC codes for channel coding in DP_LDPC systems over BF channels. Then, we design a modified joint protograph extrinsic information transfer (JPEXIT) algorithm to calculate the decoding threshold of this system. utilizing the modified JPEXIT algorithm, to improve the error performance of the system. The traditional root protograph LDPC (RPLDPC) code for this system has been redesigned. The research results display that the systems with improved RPLDPC codes have lower decoding thresholds and faster convergence trend than existing RPLDPC codes and PLDPC codes.

DOI
10.1109/jcice59059.2023.00021

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Double protograph low-density parity-check (DP-LDPC) codes based on the joint source channel coding (JSCC) system has been demonstrated to have outstanding error performance over additive white Gaussian noise (AWGN) channels. However, because of the non-ergodic nature of the block-fading (BF) channels, the protograph low-density parity-check (PLDPC) codes cannot perform well over BF channel. Whereby the excellent error performance of root protograph LDPC (RPLDPC) codes under BF channel, we utilize RPLDPC codes for channel coding in DP_LDPC systems over BF channels. Then, we design a modified joint protograph extrinsic information transfer (JPEXIT) algorithm to calculate the decoding threshold of this system. utilizing the modified JPEXIT algorithm, to improve the error performance of the system. The traditional root protograph LDPC (RPLDPC) code for this system has been redesigned. The research results display that the systems with improved RPLDPC codes have lower decoding thresholds and faster convergence trend than existing RPLDPC codes and PLDPC codes.
Forward error correcting (FEC) codes are used in many communication standards with a wide range of requirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose a novel category of low-density parity-check (LDPC) codes, based on protograph codes with local irregularity. This new code family generalizes conventional protograph-based LDPC codes and is capable of reducing the iterative decoding threshold of the conventional counterpart. We introduce an adapted version of the protograph extrinsic information transfer (PEXIT) algorithm to estimate decoding thresholds on the binaryinput additive white Gaussian noise channel, perform optimizations on the local irregularity, and simulate the performance of some constructed codes.
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.
Protograph low-density-parity-check (LDPC) codes are considered to design near-capacity low-rate codes over the binary erasure channel and the binary additive white Gaussian noise channel. For protographs with degree-one variable nodes and doubly-generalized LDPC (DGLDPC) codes, conditions are derived to ensure the 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.
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.
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 formedprotograph-basedLDPC 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.
In this paper, a new systematic construction of optimized protograph generalized low-density parity-check codes with good decoding threshold and low error floor is proposed. First, a typical code graph is generated by combining an accumulate-repeat-accumulate seed protograph with a Tanner graph extension of a simple linear block node. Subsequently, it is analyzed and optimized theoretically, especially with the puncture mechanism, by a modified extrinsic information transfer chart and an asymptotic weight distribution. The generated graph is then extended to a base matrix by a copy-and-permute procedure, accompanied with the matrix split, which is optimized by a progressive edge growth for good randomness and girth property. Finally, the proposed code matrix is created by replacing “1”in the above base matrix with square circulant sub-matrices, the offsets of which are searched by a quasi-cyclic (QC)-oriented modified approximate cycle extrinsic message degree algorithm to improve the cycle relationship, especially for the compound cycles. Simulation results show that the codes exhibit excellent performance in both error floor and waterfall region on an additive white Gaussian noise channel. Moreover, they are also characterized by faster encoding due to the QC structure as well as lower decoding complexity and less latency, which make them a natural fit for new-generation power constrained wireless communications.