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IEEE/CIC International Conference on Communications in China (ICCC)

Layered PEXIT-based Optimization of Puncturing Patterns for 5G-LDPC Codes in Few-Iteration Decoding

Qiushi Xu, Ming Jiang, Qiang Wang

Published Aug 10, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/icccworkshops67136.2025.11148138

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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.
To meet the stringent high-throughput demands of enhanced mobile broadband (eMBB), low-density parity-check (LDPC) decoding is limited to few iterations. This constraint usually degrades error-correcting performance, rousing a critical need for puncturing towards algorithmic enhancements. However, existing puncturing methods lack modulation and rate compatibility, converging to local optima due to greedy search strategies. To this end, this paper proposes a modulation and rate compatible puncturing (MrcPunc) for 5G LDPC codes. It incorporates three key techniques: 1)a revised protograph-based extrinsic information transfer (PEXIT) analysisfor accurate performance prediction, 2)a progressive multi-path search (PMPS) algorithmto avoid local optima, and 3)a compatibility optimizationsupporting various modulations and code rates. The MrcPunc yields up to 0.6 dB gain over the 5G standard puncturing under few-iteration condition without extra decoding complexity. It is noted that MrcPunc guarantees robustness against both larger iteration counts and mismatched modulations, alongside reducing the average number of decoding iterations.
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 letter, we propose a two-stage method to design finite-length puncturing patterns for LDPC codes with Hadamard constraints. At the first stage, we propose the distribution of puncturing patterns and develop extrinsic information transfer functions for distribution optimization in terms of the lowest decoding threshold. At the second stage, we analyze the iterative update process of a Hadamard check node (HCN) and find that the Euclidean distance determines the reliability of its output extrinsic information. Based on this, we propose a greedy algorithm to design puncturing patterns to maximize the number of punctured variable nodes with reliable input information. Simulations verify the good performance of the Hadamard-LDPC code with our designed puncturing patterns, compared to the 5G new radio LDPC code and the same Hadamard-LDPC code with other puncturing patterns.
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, 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.