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International Journal of Wireless & Mobile Networks

Performance Analysis and Implementation for Nonbinary Quasi-Cyclic LDPC Decoder Architecture

Tony Tsang

Published Aug 31, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.5121/ijwmn.2014.6404

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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.
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.
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts when the code length is moderate. Check node processing is one bottleneck in NB-LDPC decoding. Various techniques have been proposed to simplify the check node processing. Particularly, the computation complexity can be reduced by employing an iterative forward-backward scheme. However, this scheme requires large memory to store intermediate results. In this paper, a novel check node processing scheme and corresponding VLSI architectures are proposed for the Min-max NB-LDPC decoding. The proposed scheme first chooses a limited number of variable-to-check messages, then the check-to-variable messages to all connected variable nodes are generated independently. Employing the proposed architecture, the area requirement of the check node processing for an (837, 726) NB-LDPC code over GF (25) can be reduced to 22.5% of that of the previous work with the same processing speed and error-correcting performance.
Compared to binary low-density parity-check (LDPC) codes, nonbinary (NB) LDPC codes can achieve higher coding gain when the codeword length is moderate, but at the cost of higher decoding complexity. One major bottleneck of NB-LDPC decoding is the complicated check node processing. In this paper, a novel relaxed check node processing scheme is proposed for the min-max NB-LDPC decoding algorithm. Each finite field element of GF(2p) can be uniquely represented by a linear combination of p independent field elements. Making use of this property, an innovative method is developed in this paper to first find a set of the p most reliable variable-to-check messages with independent field elements, called the minimum basis. Then, the check-to-variable messages are efficiently computed from the minimum basis. With very small performance loss, the complexity of the check node processing can be substantially reduced using the proposed scheme. In addition, efficient VLSI architectures are developed to implement the proposed check node processing and the overall NB-LDPC decoder. Compared to the most efficient prior design, the proposed decoder for a (837, 726) NB-LDPC code over GF(25) can achieve 52% higher efficiency in terms of throughput-over-area ratio.
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 at the cost of higher decoding complexity. The high complexity is mainly caused by the complicated computations in the check node processing and the large memory requirement. In this paper, a novel check node processing scheme and corresponding VLSI architectures are proposed for the Min-max NB-LDPC decoding algorithm. The proposed scheme first sorts out a limited number of the most reliable variable-to-check (v-to-c) messages, then the check-to-variable (c-to-v) messages to all connected variable nodes are derived independently from the sorted messages without noticeable performance loss. Compared to the previous iterative forward-backward check node processing, the proposed scheme not only significantly reduced the computation complexity, but eliminated the memory required for storing the intermediate messages generated from the forward and backward processes. Inspired by this novel c-to-v message computation method, we propose to store the most reliable v-to-c messages as “compressed” c-to-v messages. The c-to-v messages will be recovered from the compressed format when needed. Accordingly, the memory requirement of the overall decoder can be substantially reduced. Compared to the previous Min-max decoder architecture, the proposed design for a (837, 726) code overGF(25) can achieve the same throughput with only 46% of the area.
When the code length is moderate, non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts at the cost of higher decoding complexity. The check node processing is a major bottleneck of NB-LDPC decoding. Its computation complexity can be reduced by an iterative forward-backward scheme. Nevertheless, large memory is required in this scheme to store intermediate results. In this paper, a novel check node processing scheme and corresponding VLSI architectures are proposed for the Min-max NB-LDPC decoding. The proposed scheme first sorts out a limited number of the most reliable input messages. Then the forward and backward processes are carried out using only these messages. In addition, an innovative approach is developed to derive the output messages from only a small number of intermediate results without noticeable performance loss. Accordingly, both the memory requirement and computation complexity are greatly reduced. For an example (837, 726) NB-LDPC code over GF(25), our proposed check node processing architecture can achieve at least 34% area reduction and about the same throughput compared to previous efforts based on the original forward-backward scheme.
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.