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IEEE Transactions on Circuits and Systems I Regular Papers

Efficient Decoder Design for Nonbinary Quasicyclic LDPC Codes

Jun Ting Lin, Jin Sha, Zhongfeng Wang, Li Li

Published May 1, 2010• 69 citations
Publisher

Abstract

This paper addresses decoder design for nonbinary quasicyclic low-density parity-check (QC-LDPC) codes. First, a novel decoding algorithm is proposed to eliminate the multiplications over Galois field for check node processing. Then, a partially parallel architecture for check node processing units and an optimized architecture for variable node processing units are developed based on the new decoding algorithm. Thereafter, an efficient decoder structure dedicated to a promising class of high-performance nonbinary QC-LDPC codes is presented for the first time. Moreover, an ASIC implementation for a (620, 310) nonbinary QC-LDPC code decoder over GF(32) is designed to demonstrate the efficiency of the presented techniques.

DOI
10.1109/tcsi.2010.2046196

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IEEE Transactions on Circuits and Systems I Regular Papers•Nov 30, 2010•58 citations
This paper addresses decoder design for nonbinary quasicyclic low-density parity-check (QC-LDPC) codes. First, a novel decoding algorithm is proposed to eliminate the multiplications over Galois field for check node processing. Then, a partially parallel architecture for check node processing units and an optimized architecture for variable node processing units are developed based on the new decoding algorithm. Thereafter, an efficient decoder structure dedicated to a promising class of high-performance nonbinary QC-LDPC codes is presented for the first time. Moreover, an ASIC implementation for a (620, 310) nonbinary QC-LDPC code decoder over GF(32) is designed to demonstrate the efficiency of the presented techniques.
This paper addresses decoder design for nonbinary quasicyclic LDPC(QC-LDPC) codes based on the extended min-sum(EMS) algorithm.It is necessary to perform quantities of recursive computation among the message vector,and only one single step operations is utilized to complete the check node update,which leads to larger decoder latency.In this paper,the novel non-binary LDPC decoder architecture is proposed to overcome this problem.Based on the rules of forward-backward algorithm,we utilize three single step operations to complete the check node update and optimize the check node update step operation.The hardware resource consumption for check node update increases slightly,but the cycle required is reduced to 1/3 of general decoder structure.The variable node update unit with fully parallel computation is presented without forward-backward,which removes recursive computation among the message vector and is of low complexity and latency.Moreover,an FPGA implementation for a(480,360) nonbinary QC-LDPC code decoder over GF(16) is designed to demonstrate the efficiency of the presented techniques.Simulation results show that the proposed design scheme can triple throughput of the decoder at the cost of less hardware resource consumption.
Non-binary low-density parity check (NB-LDPC) codes are an extension of binary LDPC codes with significantly better performance.Although various kinds of low-complexity iterative decoding algorithms have been proposed, there is a big challenge for VLSI implementation of NBLDPC decoders due to its high complexity and long latency.In this brief, highly efficient check node processing scheme, which the processing delay greatly reduced, including Min-Max decoding algorithm and check node unit are proposed.Compare with previous works, less than 52% could be reduced for the latency of check node unit.In addition, the efficiency of the presented techniques is design to demonstrate for the (620, 310) NB-QC-LDPC decoder.
Nonbinary low-density parity-check (LDPC) codes are of great interest due to their better performance cover binary ones when the code length is moderate. However, the cost of decoder implementation for these LDPC codes is still very high. In this paper, a low-complexity VLSI architecture for nonbinary LDPC decoders is presented. By exploiting the intrinsic shifting and symmetry properties of nonbinary quasi-cyclic LDPC (QC-LDPC) codes, significant reduction of memory size and routing complexity can be achieved. These unique features lead to two network-efficient decoder architectures for Class-I and Class-II nonbinary QC-LDPC codes, respectively. Comparison results with the state-of-the-art designs show that for the code example of the 64-ary (1260, 630) rate-0.5 Class-I code, the proposed scheme can save up to 70.6% hardware required by switch network, which demonstrates the efficiency of the proposed technique. The proposed design for the 32-ary (992, 496) rate-0.5 Class-II code can achieve a 93.8% switch network complexity reduction compared with conventional approaches. Furthermore, with the help of a generator for possible solution sequences, both forward and backward steps can be eliminated to offer processing convenience of check node unit (CNU) blocks. Results show the proposed 32-ary (992, 496) rate-0.5 Class-II decoder can achieve 4.47 Mb/s decoding throughput at a clock speed of 150 MHz.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate. For the first time, this paper proposes a partial-parallel decoder architecture based on the Min-max algorithm for quasi-cyclic NB-LDPC codes. A novel boundary tracking based scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In addition, layered decoding is applied, and the hardware units are optimized to reduce the latency and area. This paper also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity analysis, the proposed decoder with 5 iterations for a (837,726) code over GF(25) can easily achieve 60 Mbps throughput on ASIC devices. It is 40% more efficient than prior designs.
In this brief, a shuffled schedule (SS) of the min-max decoding algorithm is proposed for nonbinary low-density parity-check (LDPC) codes. To increase the throughput and reduce the memory requirement, a modified SS (MSS) with much simpler check node processing is also proposed, based on a new shuffled merge algorithm. Numerical simulations for three LDPC codes with different lengths and rates over GF(32) show: 1) both SS and MSS converge faster and have slightly better error performance than the flooding schedule, and 2) the degradation of the MSS in error performance as well as convergence rate is negligible. Finally, an efficient decoder architecture based on the MSS is proposed for quasi-cyclic LDPC codes. The proposed decoder architecture further enhances the decoding throughput with improved check and variable node processing units. The implementation results of an (837, 726) LDPC decoder over GF(32) demonstrate that the proposed architecture outperforms those in previous works.
Nonbinary low-density parity-check (NB-LDPC) codes constructed over GF(q) (q >; 2) can achieve higher coding gain than binary LDPC codes when the code length is moderate. A complete partial-parallel decoder architecture based on the Min-max algorithm is proposed for quasi-cyclic NB-LDPC codes in this paper. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm5) has also been synthesized on a Xilinx Virtex-2 Pro FPGA device. It can achieve a throughput of 9.30 Mbps when 15 decoding iterations are carried out.