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IEEE International Symposium on Information Theory (ISIT)

Protograph-Based LDPC Codes with Local Irregularity

Vincent Wüst, Erdem Eray Cil, Laurent Schmalen

Published Jun 22, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/isit63088.2025.11195381

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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 an innovative LDPC coded modulation scheme. We design binary low density parity check (LDPC) codes that are combined with high level modulations such as 8PSK and 16QAM with and without a channel interleaver. At the receiver a demapper transforms the received inphase and quadrature samples to produce reliability information that feeds the binary LDPC decoder. Using this scheme, the same encoder and decoder can support various modulations. Analysis of ensemble average weight enumerators shows that the minimum distance of the proposed LDPC codes grows linearly with block size. Our constructions are based on protograph structures that support high-speed decoder implementations. We also show that precoding can be used to lower the threshold of LDPC codes. The decoding thresholds of the proposed codes, which have linearly increasing minimum distance in block size, outperform that of regular LDPC codes. Furthermore, a family of low to high rate codes, with thresholds that adhere closely to their respective channel capacity thresholds, is presented. For maximum variable node degree 6, the iterative decoding thresholds of these codes outperform the best known unstructured irregular LDPC codes reported in the literature. Iterative decoding simulation results are provided for BPSK, QPSK, 8PSK, and 16QAM modulations over the additive white Gaussian noise channel. FPGA simulation results for the proposed LDPC codes with input block size of 4096 and QPSK modulation (throughput=1 bps/Hz) show that a frame error rate of 10-8and a bit error rate of 10-10can be achieved at Eb/No=1.50 dB
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.
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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.
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The protograph low‐density parity‐check (LDPC) codes possess many attractive properties, such as the low encoding/decoding complexity and better error floor performance, and hence have been successfully applied to different types of communication and data storage channels. In this study, the authors design protograph LDPC codes for communication systems corrupted by the impulsive noise, which are modelled as additive white symmetric alpha‐stable noise (AWS SN) channels. They start by presenting a novel simulation‐based protograph extrinsic information transfer analysis to derive the iterative decoding threshold of the protograph codes. By further applying the asymptotic weight distribution analysis, the authors design new protograph codes for the AWS SN channel. Both theoretical analysis and simulation results demonstrate that the proposed protograph codes can provide better error rate performance than the prior art AR4JA code, the irregular codes optimised for the AWGN channel, as well as the irregular codes optimised for the AWS SN channel.