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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Complexity-Reducing Algorithm for Serial Scheduled Min-Sum Decoding of LDPC Codes

Hironori Uchikawa, Kohsuke Harada

Published Jan 1, 2009• 1 citation
Publisher

Abstract

We propose a complexity-reducing algorithm for serial scheduled min-sum decoding that reduces the number of check nodes to process during an iteration. The check nodes to skip are chosen based on the reliability, a syndrome and a log-likelihood-ratio (LLR) value, of the incoming messages. The proposed algorithm is evaluated by computer simulations and shown to reduce the decoding complexity about 20% compared with a conventional serial scheduled min-sum decoding with small fractional decibel degradation in error correction performance.

DOI
10.1587/transfun.e92.a.2411

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We propose a complexity-reducing algorithm for serial scheduled min-sum decoding that reduces the number of check nodes to process during an iteration. The check nodes to skip are chosen based on the reliability, a syndrome and a log-likelihood-ratio (LLR) value, of the incoming messages. The proposed algorithm is evaluated by computer simulations and shown to reduce the decoding complexity about 20% compared with a conventional serial scheduled min-sum decoding with small fractional decibel degradation in error correction performance.
We propose a complexity-reducing method for serial min-sum decoding that reduces the number of check nodes to process during an iteration. The check nodes to skip are chosen based on the reliability, a syndrome and a log-likelihood-ratio (LLR) value, of the incoming messages. The proposed method is evaluated by computer simulations and shown to reduce the decoding complexity up to 70 % compared with conventional serial min-sum decoding with small fractional decibel degradation in error correction performance.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.
Various log-likelihood-ratio-based belief-propagation (LLR-BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representations of the decoding computations are shown to achieve a reduction in complexity by simplifying the check-node update, or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from performance, latency, computational-complexity, and memory-requirement perspectives.
Compared to classic channel coding,Low-density parity-check(LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications.However,as maximum-likelihood decoding is too complex to implement,suboptimal decoders have to be employed.One of the most popular decoding algorithms of LDPC codes is belief propagation(BP) decoding.Informed Dynamic Scheduling(IDS) can provide a better BER performance,but hard to implement due to high computational complexity increased.In order to improve the convergence,a simple low-complexity sequential check-node-based scheduling strategy is proposed.A new check-node-based reliability measure is defined,which represents the degree of reliability approximately.The reliability measure is used for ordering while the actual message updates still use the exact BP equations.During an iteration,the schedule strategy finds an update sequence,which is arranged by the new defined reliability measure in ascending order.Complexity is compared among those algorithms.Mechanism why the new strategy works effective is presented.Simulation shows that the new approach significantly improves the BER performance using short-length block LDPC codes and reduces iterations.
Two methods are proposed to reduce the complexity of the belief propagation (BP) decoding for low-density parity-check (LDPC) codes, with the focus on the layered decoding for quasi-cyclic LDPC (QC-LDPC) codes. The two methods can be separately incorporated into the layered decoding procedures and combined seamlessly to provide the two-fold complexity reduction. In the first method, the message updates regarding a subset of variable nodes are omitted. To construct the subset, the most reliable bit-level channels, derived fromM-ary input channels, are identified. Then, we select the variable nodes with initial log-likelihood ratios (LLRs) exceeding a threshold among the ones assigned to the most reliable bit-level channels to form the subset. The threshold is designed and adjusted based on characteristics of the most reliable bit-level channels. Our numerical results demonstrate that the first method significantly reduces the complexity with negligibly impacting the error-correcting performance. In the second method, each layer of base graphs of QC-LDPC codes uses either sum-product algorithm (SPA) or min-sum algorithm (MSA) to update LLRs. A degree-based algorithm is presented to determine the layers employing either SPA or MSA. We compare with two intuitive methods: 1) applying SPA to randomly selected layers and MSA to the remaining layers, and 2) applying SPA to the core layers of 5G NR LDPC codes and MSA to the remaining layers. According to the numerical results, the degree-based algorithm maximally reduces the complexity while maintaining the same performance. To evaluate the joint method, the first method is applied on top of the second method. Further complexity reduction is achieved without degrading the performance of the second method.