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IEEE Transactions on Communications

MrcPunc: Modulation and Rate Compatible Puncturing for Few-Iteration 5G LDPC Decoding

Qiushi Xu, Huayi Zhou, Mingyang Zhu, Ming Jiang, Chuan Zhang

Published Jan 1, 2026• 4 citations
Publisher

Abstract

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.

DOI
10.1109/tcomm.2026.3677140

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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 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.
The new 5G communications standard increases data rates and supports low-latency communication that places constraints on the computational complexity of channel decoders. 5G low-density parity-check (LDPC) codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. Practical LDPC decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. Performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing lookup tables that replace conventional finite-precision node computations. The IB approach exchanges messages represented by integers with very small bit width. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include puncturing and rate-compatible IB decoder design. As an example of the new approach, a 4-bit information bottleneck decoder is evaluated for PBRL LDPC codes over a typical range of rates. Frame error rate simulations show that the proposed scheme outperforms offset min-sum decoding algorithms and operates very close to double-precision sum-product belief propagation decoding.
Abstract In order to cater to the needs of the 5G standard, one of the prominent solutions in terms of high coding gain, high throughput and low power dissipation is the 5G NR LDPC (New Radio Low Density Parity Check) codes which have been adopted by 5G Standard. LDPC codes are the successful Third Generation Forward Error Correcting codes. An Efficient decoder is the key to the success of any Error Correcting Code. LDPC codes are one whose parity check matrix have a very few non zero entries. 5G NR LDPC codes are constructed by Protographs or base graphs and are block structured. This paper improves the performance of Layered Iterative minsum Approximation Message Passing decoding Algorithm using Rate Matching, Fixed Point Quantization and Offset minsum techniques. Rate Matching is to maintain the exact number of encoded blocks with in the TTI. Simulation of this algorithm with BPSK encoding over AWGN channel shows that BER of 10-3 gives Eb/No of~2 dB for the block length of 105.
This paper presents a cycle-based rate-compatible puncturing technique for non-binary (NB) low-density parity-check (LDPC) codes. The proposed puncturing technique is based on the connectivity of the short non-binary (NB) cycles present in the Tanner graph. The connectivity of a cycle is measured by the extrinsic message degree (EMD). The short cycles with low values of EMD degrade the performance of iterative decoders significantly. The proposed technique selects the variable nodes for puncturing by reckoning their involvements in the short NB cycles with a low EMD. Simulations in different contexts are performed to check the efficiency of the proposed technique.
This work investigated the performance of a newly developed protograph-based low-density parity-check code (LDPC) families belonging to accumulate-repeat-4-jagged-accumulate codes. The proposed code has hierarchical irregularity and quasi-cyclic property that retains it to be suitable for fast encoder and decoder implementation. The code used in this work is a rate-compatible linearly punctured code. The modified iterative decoding algorithm as mentioned in the literature is used along with a newly proposed encoder and simulation has been done for proposed LDPC coded orthogonal frequency division multiplexing (OFDM) link over wireless and optical wireless channels with hard- and soft-decision decoding. The code relates to new methods for designing rate-compatible families of protographs of different rates, all having the linear minimum distance property showing small performance degradation compared with the threshold. The parity-check matrix is composed of small identical modules to reduce the routing complexity of the decoder. The main essence of this code lies in the fact that LDPC codes of arbitrarily large size can be built by expanding from individual protographs or rate-compatible protograph families.
Increased data rates and very low-latency requirements place strict constraints on the computational complexity of channel decoders in the new 5G communications standard. Practical low-density parity-check (LDPC) decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. In turn, performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing mappings that replace conventional finite-precision node computations. As a result, the exchanged messages in the IB approach can be represented with a very small number of bits. 5G LDPC codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include IB decoder design for puncturing and rate-compatibility. In contrast to existing IB decoder design techniques, the proposed decoder can be used for a large range of code rates with a static set of optimized mappings. The proposed construction approach is evaluated for a typical range of code rates and bit resolutions ranging from 3 bit to 5 bit. Frame error rate simulations show that the proposed scheme always outperforms min-sum decoding algorithms and operates close to double-precision sum-product belief propagation decoding. Furthermore, alternatives to the lookup table implementations of the mutual-information-maximizing mappings are investigated.