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Asian Conference on Defence Technology

An improvement of decoding time of ordered statistic decoding for medium length LDPC codes

Yuki Kawauchi, Kohtaro Watanabe, Seiji Kataoka

Published Nov 1, 2017• 0 citations
Publisher

Abstract

It is well-known that the Sum-Product Algorithm (SPA) is an efficient algorithm for decoding Low Density Parity Check (LDPC) codes. In spite of this, for LDPC codes with medium length which are now attracting interests for the application to fifth generation systems, it is known that decoding error rate is much inferior to that of Maximum Likelihood Decoding (MLD). In this paper, we improve bit error rate of SPA with so called Ordered Statistic Decoding (OSD) method by Fossorier [1]D Especially, we improve stopping condition of combinatorial search in OSD method and demonstrate by simulation that the proposal stopping condition is more efficient compared to Fossorier (IEEE J. Sel. Areas Commun., 19, 2001). For that purpose, we introduce a conception “coincidence rate” which plays an important role.

DOI
10.1109/acdtj.2017.8259607

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It is well-known that the Sum-Product Algorithm (SPA) is an efficient algorithm for decoding Low Density Parity Check (LDPC) codes. In spite of this, for LDPC codes with medium length which are now attracting interests for the application to fifth generation systems, it is known that decoding error rate is much inferior to that of Maximum Likelihood Decoding (MLD). In this paper, we improve bit error rate of SPA with so called Ordered Statistic Decoding (OSD) method by Fossorier [1]D Especially, we improve stopping condition of combinatorial search in OSD method and demonstrate by simulation that the proposal stopping condition is more efficient compared to Fossorier (IEEE J. Sel. Areas Commun., 19, 2001). For that purpose, we introduce a conception “coincidence rate” which plays an important role.
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and ordered statistics decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced by mBP, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order- (m -1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.
We present in this paper a new method for improving the decoding of the LDPC (low-density parity check) codes by optimising the log-SPA (sum-product algorithm). Currently, the LDPC codes give very good results with iterative decoding algorithm, log-SPA, based on the propagation confidence BP (belief propagation). To improve the existing log-SPA, we propose a decoding algorithm (log-SPA modified), which minimises the error decoding of words that could not be previously decoded. This algorithm is based on the dependency between the weight of the syndrome and the weight of the error sequence generated during iterations of decoding. Simulations illustrate the performance of our approach compared with classical LDPC code based on log-SPA.
After the introduction of iterative coding, Low Density Parity Check (LDPC) codes have received a lot of attention due to their remarkable near Shannon-limit performance and practical decoder implementation. However, when employing an LDPC code for various applications, multiple issues do arise at the simulation, algorithm and implementation levels. The first issue is the performance evaluation of the iterative LDPC decoder in the very low Bit Error Rate (BER) regions. So far, no analytical tool has been developed to evaluate the performance of LDPC codes. Unfortunately standard Monte Carlo (MC) simulations cannot be used for performance estimation in these low BER regions due to prohibitive execution times. The second issue is the efficiency of the decoding algorithm. Due to the presence of short cycles in the bipartite graph, sum-product decoding algorithms lead to considerable performance loss for short block-length LDPC codes and produce error floors for longer codes. In addition, the iterative processing and estimation of soft probabilistic values with these algorithms result in very high computational complexity, which in turn impedes the adoption of LDPC codes for power constrained systems. Another prime objective is to design a high throughput decoder architecture which is capable of supporting multiple rates and variable code lengths within minimal area. This work aims to address and provide solutions to the above problems. As a solution to the performance estimation problem of LDPC codes, a highly efficient and novel fast BER simulation technique is developed. At the algorithm level, a performance improvement and error floor avoidance method is introduced, and a computationally efficient algorithm is developed for the sum-product decoding of LDPC codes. And finally, at the architecture level, a high throughput multi-rate variable code length implementation is presented which, when implemented, efficiently minimizes device resources while alleviating the routing complexity of the decoder.
Low-density parity-check (LDPC) codes are widely used in communication systems. When user messages are encoded by binary LDPC codes and transmitted with higher-order modulations, bits composing the same modulated symbol are generally correlated. Traditional soft-decision decoding algorithms for binary LDPC codes like sum-product algorithm (SPA) and min-sum algorithm (MSA) update messages only based on log-likelihood ratio (LLR) of bits, and correlations introduced by modulation are not utilized. In this paper, symbol-based SPA and MSA (S-SPA and S-MSA) which incorporate symbol-level information in the decoding procedures are proposed to provide an alternative low-cost way to better utilize available information. By narrowing the search space of symbols based on bit-level information, the complexities of the proposed algorithms are independent of modulation order. S-SPA and S-MSA achieve better error-correction performances than SPA and MSA with little additional complexities and S-MSA is friendly to hardware design of LDPC decoder.