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IEEE Communications Letters

Design of Protograph-Based LDPC Codes with Limited Decoding Complexity

Chengjun Tang, Ming Jiang, Chunming Zhao, Hong Shen

Published Sep 29, 2017• 17 citations
Publisher

Abstract

In this letter, we present a design method to find good protograph-based low-density parity-check codes with the numbers of nonzero elements in the parity-check matrix and decoding iterations both strictly limited. We utilize the protograph-based extrinsic information transfer (PEXIT) analysis to evaluate the error performance and employ the differential evolution algorithm to devise a well-performed coding scheme. In particular, the number of iterations in the PEXIT analysis is set to a small value due to the limited iterations in the decoding process. Both numerical analyses and simulations verify that the resulting codes exhibit better performance than conventional code designs under the limitation of decoding complexity.

DOI
10.1109/lcomm.2017.2757941

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In this letter, we present a design method to find good protograph-based low-density parity-check codes with the numbers of nonzero elements in the parity-check matrix and decoding iterations both strictly limited. We utilize the protograph-based extrinsic information transfer (PEXIT) analysis to evaluate the error performance and employ the differential evolution algorithm to devise a well-performed coding scheme. In particular, the number of iterations in the PEXIT analysis is set to a small value due to the limited iterations in the decoding process. Both numerical analyses and simulations verify that the resulting codes exhibit better performance than conventional code designs under the limitation of decoding complexity.
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, an early stopping scheme is proposed for low-density parity-check (LDPC) decoders. The proposed scheme predicts that the LDPC decoder will not be able to correct errors and then stops the iterative decoding process before reaching the maximum number of iterations. When the number of parity checks unsatisfied at both the l-th and the (l-T)-th decoding iterations is larger than a threshold, the decoder with the proposed scheme predicts that the decoding of the codeword is failed at the last iteration. Protograph-based extrinsic information transfer (PEXIT) chart analysis is used to determine the threshold. Simulation results show that the LDPC decoder can correct errors with the lower average number of iterations by using both the conventional syndrome test and proposed scheme.
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.
In this paper, an innovative method to optimize the puncturing patterns of the 5G low-density parity-check codes, which leverages layered protograph-based extrinsic information transfer (PEXIT) analysis to evaluate decoding performance and the progressive multi-path search (PMPS) algorithm to optimizing puncturing patterns. Compared with existing methods, layered PEXIT analysis is faster and more accurate, while the PMPS algorithm effectively addresses the local optimum trap commonly encountered by greedy algorithms. Simulation results demonstrate that using optimized puncturing patterns significantly improve the few-iteration decoding performance, thereby enhancing the reliability of resource-constrained communication systems without introducing any additional complexity.
This paper designs two protograph LDPC codes with code-rate R>1/2R > 1/2R>1/2. A simple method using the protograph extrinsic information transfer (PEXIT) to design the codes with a low decoding threshold and the asymptotic weight enumerator (AWE) to evaluate the error floor of the codes is deployed. Simulation results show that the proposed codes have a better error floor than prior art protograph codes and offer higher rate protographs.
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.