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arXiv:1111.0703 · IEEE International Symposium on Circuits and Systems proceedings

Efficient network for non-binary QC-LDPC decoder

Chuan Zhang, Jin Sha

Published May 1, 2012• 1 citation
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Abstract

This paper presents approaches to develop efficient network for non-binary quasi-cyclic LDPC (QC-LDPC) decoders. By exploiting the intrinsic shifting and symmetry properties of the check matrices, significant reduction of memory size and routing complexity can be achieved. Two different efficient network architectures for Class-I and Class-II non-binary QC-LDPC decoders have been proposed, respectively. Comparison results have shown that for the code of the 64-ary (1260, 630) rate-0.5 Class-I code, the proposed scheme can save more than 70.6% hardware required by shuffle network than the state-of-the-art designs. The proposed decoder example for the 32-ary (992, 496) rate-0.5 Class-II code can achieve a 93.8% shuffle network reduction compared with the conventional ones. Meanwhile, based on the similarity of Class-I and Class-II codes, similar shuffle network is further developed to incorporate both classes of codes at a very low cost.

DOI
10.1109/iscas.2012.6271842

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This paper presents approaches to develop efficient network for non-binary quasi-cyclic LDPC (QC-LDPC) decoders. By exploiting the intrinsic shifting and symmetry properties of the check matrices, significant reduction of memory size and routing complexity can be achieved. Two different efficient network architectures for Class-I and Class-II non-binary QC-LDPC decoders have been proposed, respectively. Comparison results have shown that for the code of the 64-ary (1260, 630) rate-0.5 Class-I code, the proposed scheme can save more than 70.6% hardware required by shuffle network than the state-of-the-art designs. The proposed decoder example for the 32-ary (992, 496) rate-0.5 Class-II code can achieve a 93.8% shuffle network reduction compared with the conventional ones. Meanwhile, based on the similarity of Class-I and Class-II codes, similar shuffle network is further developed to incorporate both classes of codes at a very low cost.
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.
The recently proposed single block-row quasi-cyclic low-density parity-check (QC-LDPC) codes are favorable for high-speed applications. However, conventional decoder design methods are not suitable for this kind of codes. To tackle this issue, this paper aims at designing efficient column-layered single block-row QC-LDPC decoder architecture without affecting the decoding performance. Moreover, the simplified version which only requires single minimum value is also proposed for further hardware reduction. Results show that, for the rate-0.9006 (1640, 1477) single block-row QC-LDPC code, the proposed two designs achieves significant advantages in both hardware and latency over their row-layered counterpart.
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.
The design of a high-speed decoder using traditional partly parallel architecture for Non-Quasi-Cyclic (NQC) Low-Density Parity-Check (LDPC) codes is a challenging problem due to its high memory-block cost and low hardware utilization efficiency. In this paper, we present efficient hardware implementation schemes for NQCLDPC codes. First, we propose an implementation-oriented construction scheme for NQC-LDPC codes to avoid memory-access conflict in the partly parallel decoder. Then, we propose a Modified Overlapped Message-Passing (MOMP) algorithm for the hardware implementation of NQC-LDPC codes. This algorithm doubles the hardware utilization efficiency and supports a higher degree of parallelism than that used in the Overlapped Message Passing (OMP) technique proposed in previous works. We also present single-core and multi-core decoder architectures in the proposed MOMP algorithm to reduce memory cost and improve circuit efficiency. Moreover, we introduce a technique called the cycle bus to further reduce the number of block RAMs in multi-core decoders. Using numerical examples, we show that, for a rate-2/3, length-15360 NQC-LDPC code with 8.43-dB coding gain for Binary PhaseShift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel, the decoder with the proposed scheme achieves a 23.8%-52.6% reduction in logic utilization per Mbps and a 29.0%-90.0% reduction in message-memory bits per Mbps.
Abstract Layered decoding (LD) of Low-Density Parity-Check (LDPC) codes is a decoding schedule that facilitates partially parallel architectures for performing Belief Propagation (BP)-based iterative algorithms. It has reduced implementation complexity and memory overhead compared to fully parallel architectures and higher convergence speed compared to both serial and parallel architectures. In this paper, we introduce a modified form of shuffling of the Parity-Check Matrices (PCMs) of Quasi-Cyclic LDPC (QC-LDPC) codes, which is basically an interleaving operation of the rows of the PCM. The modified shuffling method just like the conventional shuffling method results in a PCM in which each layer can be produced by the circulation of its above layer one symbol to the right. However, it additionally guarantees the weights of the columns in each layer to be either zero or one. Then, we show that due to these two properties, the number of occupied Look-Up Tables (LUTs) on a Field Programmable Gate Array (FPGA) is reduced by about 93% and consumed on-chip power by nearly 80%. Nevertheless, shuffling doesn’t degrade Bit Error Rate (BER) performance compared with the non-shuffled case. Additionally, decoding throughput is not sacrificed for low SNR values and its degradation is negligible until the BER of 1e-6.
This paper studies low-complexity high-speed decoder architectures for quasi-cyclic low density parity check (QC-LDPC) codes. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. Enhanced partially parallel decoding architectures are proposed to linearly increase the throughput of conventional partially parallel decoders through introducing a small percentage of extra hardware. Based on the proposed architectures, a (8176, 7154) Euclidian geometry-based QC-LDPC code decoder is implemented on Xilinx field programmable gate array (FPGA) Virtex-II 6000, where an efficient nonuniform quantization scheme is employed to reduce the size of memories storing soft messages. FPGA implementation results show that the proposed decoder can achieve a maximum (source data) decoding throughput of 172 Mb/s at 15 iterations