Research of LDPC Decoding Algorithms for New-generation Digital Communication System

Li Hua Xu, Daoxing Guo, Chunqiang Shi

Abdel Halim A. Zikry, Ashraf Yehya Hassan, Wageda I. Shaban +1 more

Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, like DVB-S2 and WLAN802.1..This paper aims to know what is LDPC,what its application and introduce encoding algorithms that gives rise to a linear encoding time and also show that the regular and irregular LDPC performance and also introduce different methods for decoding LDPC. I discuss in detail LDPC decoding algorithm: bit flipping algorithm, as a type from hard decision .belief propagation algorithm, sum product algorithm and minimum sum algorithm as examples from soft decision .I expect that at least some students or researchers involved in researching LDPC codes would find this paper helpful.

Michaelraj Kingston Roberts

Rong Chen, Lan Chen

Fifth generation (5G) is a new generation mobile communication system developed for the growing demand for mobile communication. Channel coding is an indispensable part of most modern digital communication systems, for it can improve the transmission reliability and anti-interference. In order to meet the requirements of 5G communication, a dual threshold self-corrected minimum sum (DT-SCMS) algorithm for low-density parity-check (LDPC) decoders is proposed in this paper. Besides, an architecture of LDPC decoders is designed. By setting thresholds to judge the reliability of messages, the DT-SCMS algorithm erases unreliable messages, improving the decoding performance and efficiency. Simulation results show that the performance of DT-SCMS is better than that of SCMS. When the code rate is 1/3, the performance of DT-SCMS has been improved by 0.2 dB at the bit error rate of 10 − 4 compared with SCMS. In terms of the convergence, when the code rate is 2/3, the number of iterations of DT-SCMS can be reduced by up to 20.46% compared with SCMS, and the average proportion of reduction is 18.68%.

Massimo Rovini, Luca Fanucci, Francesco Rossi

Jinghu Chen, M.P.C. Fossorier

Iterative decoding techniques have been receiving more and more attentions with the invention of turbo codes and the rediscovery of low-density parity-check (LDPC) codes. An important aspect in the study of iterative decoding is the tradeoff between decoding performance and complexities. For both LDPC codes and turbo codes, optimum decoding algorithms can provide very good performance. However, complicated operations are involved in the optimum decoding, and prohibit the wide applications of LDPC codes and turbo codes in the next generation digital communication and storage systems. Although there exist sub-optimum decoding algorithms for both LDPC codes and turbo codes, the decoding performance is degraded with the sub-optimum algorithms, and under some circumstances, the gap is very large. This research investigates the reduced complexity decoding algorithms of LDPC codes and turbo codes. For decoding LDPC codes, new algorithms, namely the normalized BP-based algorithm and the offset BP-based algorithm, are proposed. For these two reduced complexity algorithms, density evolution algorithms are derived, and are used to determine the best decoder parameters associated with each of the algorithms. Numerical results show that the new algorithms can achieve near optimum decoding performances for infinite code lengths, and simulation results reveal the same conclusion for short to medium code lengths. In addition to the advantage of low computational complexities, the two new algorithms are less subject to quantization errors and correlation effects than the optimum BP algorithm, and consequently are more suitable for hardware implementation. For a special kind of LDPC codes - the geometric LDPC codes, we propose the normalized APP-based algorithm, which is even more simplified yet still can achieve the near optimum performance. For decoding turbo codes, two new sub-optimum decoding algorithms are proposed. The first is the bi-directional soft-output Viterbi algorithm (bi-SOVA), which is based on utilizing a backward SOYA decoding in addition to the conventional forward one, and can achieve better performance than the uni-directional SOYA. The second is the normalized Max-Log-MAP algorithm, which improves the performance of the Max-Log-MAP decoding by scaling the soft outputs with some predetermined factors.