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European Conference on Circuit Theory and Design

FPGA implementation of rate-compatible QC-LDPC code decoder

Anton Blad, Oscar Gustafsson

Published Aug 1, 2011• 6 citations
Publisher

Abstract

The use of rate-compatible error correcting codes offers several advantages as compared to the use of fixed-rate codes: a smooth adaptation to the channel conditions, the possibility of incremental Hybrid ARQ schemes, as well as simplified code representations in the encoder and decoder. In this paper, the implementation of a decoder for rate-compatible quasi-cyclic LDPC codes is considered. The decoder uses check node merging to increase the convergence speed of the algorithm. Check node merging allows the decoder to achieve the same performance with a significantly lower number of iterations, thereby increasing the throughput. The feasibility of a check node merging decoder is investigated for codes from IEEE 802.16e and IEEE 802.11n. The faster convergence rate of the check node merging algorithm allows the decoder to be implemented using lower parallelization factors, thereby reducing the logic complexity. The designs have been synthesized to an Altera Cyclone II FPGA, and results show significant increases in throughput at high SNR.

DOI
10.1109/ecctd.2011.6043844

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The use of rate-compatible error correcting codes offers several advantages as compared to the use of fixed-rate codes: a smooth adaptation to the channel conditions, the possibility of incremental Hybrid ARQ schemes, as well as sharing of the encoder and decoder implementations between the codes of different rates. In this paper, the implementation of a decoder for rate-compatible quasi-cyclic LDPC codes is considered. Assuming the use of a code ensemble obtained through puncturing of a low-rate mother code, the decoder achieves significantly reduced convergence rates by merging the check node neighbours of the punctured variable nodes. The architecture uses the minsum algorithm with serial node processing elements to efficiently handle the wide spread of node degrees that results from the merging of the check nodes.
In this paper, a new and efficient decoding architecture, Single-Scan Layer Decoding (SLD), is realized in FPGA for multi-rate Quasi-Cyclic LDPC (QC-LDPC) codes. The SLD algorithm simplifies the nodes updating process and messages storing process of the offset min-sum algorithm, speeding up the decoding process and reducing nearly a half of resources consumption. Besides, the SLD algorithm, introducing the semi-parallel architecture into decoding architecture, can increase the convergence rate by 2X and decrease the interconnect complexity of hardware implementation. For multi-rate QC-LDPC Codes in 802.11.n, comparing with float-point software implementation, the degradations of the fixed-point SLD algorithm with 10 iterations in FPGA are all less than 0.ldB and the throughput of different code rates are all above 100Mbps.
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
A multi-rate decoder of Quasi-Cyclic LDPC(QC-LDPC) decoder is presented based on the improvement of layered decoding algorithm.The implementation has larger bit throughput resulting from fast convergence speed by more than 50 percent in terms of decoding iterations.Only four memories are used to store the messages which significantly reduce the area and the power dissipation.Adjusted integer quantization of layered decoding algorithm for check-node updating reduces the complexity and the correction factor guarantees the error rate performance.The proposed decoding architecture is implemented in the standard recommended.The decoder consumes 0.6 million gates,and reaches a throughput of 134 Mb/s at a clock frequency of 110 MHz with rate of 1/2.
In this paper, we present a rate-compatible LDPC decoder architecture which supports code rates between the rate of the mother code and 1. The rate-1/2 2304-bit Quasi-Cyclic (QC) LDPC codes with dual-diagonal parity check structure is selected from WiMax standard as the mother code and is punctured using specific puncturing patterns to obtain arbitrary rates. Parallel layered decoding architecture (PLDA) is employed to reduce chip area and improve the throughput. Simulation results show that the proposed punctured codes have comparable error correcting performances with the performances of dedicated codes from WiMax standard. The decoder is implemented on the platform of Xilinx XC2V8000. Compared with previous WiMax LDPC decoders synthesized by the same device, our low-complexity decoder consumes less FPGA resources: reduction of slices by 63%, flip-flops by 73%, look-up tables (LUTs) by 60% and RAMs by 30%.
The contribution of this paper is implementing a high throughput LDPC codec in FPGA for quantum key distribution (QKD) system. By software, the throughput of error correction in QKD system via LDPC codec could only reach 1.8Mbps, which is not satisfactory for high speed QKD systems. Thus, it is desirable that LDPC error correction is realized in FPGA to increase the throughput. LDPC codec is implemented according to IEEE802.16e standard. The encoder directly uses a parity-check matrix of lower triangular structure without the construction of generator matrix, so that it effectively reduce the encoding complexity of Richardson encoding algorithm. The decoder uses the BP Min-Sum algorithm to balance performance and complexity. The codec is implemented in an Altera Arria II EP2AGX260 FPGA with a 2304-bit code length and 2/3 code rate. The partly parallel decoding structure achieves a 99.95 Mbps processing throughput on the condition that the maximum number of iterations for each code block is 20. The achievable throughput is much higher than the requirements of current QKD systems.