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IEEE International Symposium on Circuits and Systems proceedings

Efficient Message Passing Architecture for High Throughput LDPC Decoder

Zhiqiang Cui, Zhongfeng Wang

Published May 1, 2007• 14 citations
Publisher

Abstract

In this paper, we propose an efficient message passing architecture for permutation matrices based LDPC code decoders. Min-sum algorithm is reformulated to facilitate significant reduction of routing complexity and memory usage. For a (2048, 1723) (6, 32) LDPC code with 4-bit quantization, 54% outgoing wires per variable node unit and 90% outgoing wires per check node unit can be saved. To further reduce hardware complexity, an optimized nonuniform quantization scheme using only 3 bits to represent each message has been investigated. The simulation result shows that it has only 0.25dB performance loss from the floating-point SPA

DOI
10.1109/iscas.2007.378075

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In this paper, we propose an efficient message passing architecture for permutation matrices based LDPC code decoders. Min-sum algorithm is reformulated to facilitate significant reduction of routing complexity and memory usage. For a (2048, 1723) (6, 32) LDPC code with 4-bit quantization, 54% outgoing wires per variable node unit and 90% outgoing wires per check node unit can be saved. To further reduce hardware complexity, an optimized nonuniform quantization scheme using only 3 bits to represent each message has been investigated. The simulation result shows that it has only 0.25dB performance loss from the floating-point SPA
In this paper, we propose an improvement of the normalized min-sum (MS) decoding algorithm and novel MS decoder architectures with reduced word length using nonuniform quantization schemes for low-density parity-check (LDPC) codes. The proposed normalized MS algorithm introduces a more exact adjustment with two optimized correction factors for check-node-updating computations, while the conventional normalized MS algorithm applies only one correction factor. The proposed algorithm provides a significant performance gain without any additional computation or hardware complexity. The finite word-length analysis in implementing an LDPC decoder is a very important factor since it directly impacts the size of memory to store the intrinsic and extrinsic messages and the overall hardware area in the partially parallel LDPC decoder. The proposed nonuniform quantization scheme can reduce the finite word length while achieving similar performances compared to a conventional quantization scheme. From simulation results, it is shown that the proposed 4-bit nonuniform quantization scheme achieves an acceptable decoding performance, unlike the conventional 4-bit uniform quantization scheme. Finally, the proposed MS decoder architectures by the nonuniform quantization scheme provide significant reductions of 20% and up to 8% for the memory area and combinational logic area, respectively, compared to the conventional 5-bit ones.
In the recent literature, turbo decoding message passing (TDMP) or layered decoding has been proposed for the decoding of low-density parity-check (LDPC) codes using a trellis-based BCJR algorithm in check node units (CNU). We present a new architecture for supporting rate compatible array LDPC codes that uses an offset-based min-sum decoding algorithm instead of the BCJR. The proposed architecture utilizes the value-reuse properties of min-sum and block-serial scheduling of computations, along with TDMP. This novel architecture has the following features: removal of memory needed to store the sum of the variable node messages and the channel values, removal of memory needed to store the variable node messages, 40%-72% savings in storage of extrinsic messages depending on rate of the codes, reduction of routers by 50%, and increase of throughput up to 2times. Implementations on our test-bed FPGA achieve decoded throughputs up to 1.36 Gbps and 2.27 Gbps for each iteration for (5,k) and (3,k) array LDPC codes, respectively. ASIC implementation achieve decoded throughputs up to 5.9 Gbps for each iteration for (5,k) array LDPC codes.
This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity, while achieving competitive error performance compared with conventional min-max algorithm. Simulation result on a (255,175) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity non-binary LDPC (NB-LDPC) decoding algorithms. Based on this algorithm, a partial-parallel decoder architecture is implemented for cyclic NB-LDPC codes, where the variable node units are redesigned and the routing network is optimized for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.
Very high data rates and decoding computational complexity place strict constraints in 5G and 6G communications. In this paper, non-uniform Quantized Decoding algorithm is proposed for Low-density Parity Check codes (LDPC). In the proposed algorithm, the check node updating process is carried out using quantization, which reduces complexity. The Sum Product Algorithm (SPA) is iterative message passing decoding techniques offer the optimal performance for LDPC codes. Implementations use message-passing decoding with more precision, results extremely high complexity. In Iterative, message-passing (MP), trapping sets and absorbing sets causes low error floor. In this article non-uniform quantization proposed to overcome dynamic range of values over uniform quantization. Simulation results provide coding gain increases closer to of 0.5 dB in higher SNR and has good error floor at 10−5.
In this paper, we propose a turbo decoding message-passing (TDMP) algorithm to decode regular and irregular low-density parity-check (LDPC) codes. The TDMP algorithm has two main advantages over the commonly employed two-phase message-passing algorithm. First, it exhibits a faster convergence behavior (up to 50% less iterations), and improvement in coding gain (up to an order of magnitude for moderate-to-high SNR and small number of iterations). Second, the corresponding decoder architecture has a significantly reduced memory requirement that amounts to a savings of (75 + 25n//spl Sigma/ node-degrees)% > 75% for code-length n. A decoder architecture featuring the TDNW algorithm is also presented. Furthermore, we propose a new structure on the parity-check matrix of an LDPC code based on permutation matrices aimed at reducing interconnect complexity and improving decoding throughput. In addition, we construct a wide range of LDPC codes based on Ramanujan graphs which possess this structure.
In this paper, the partial-min algorithms are proposed for updating the check node messages in decoding low-density parity-check (LDPC) codes. The proposed methods can achieve a good performance-versus-complexity tradeoff by reducing both the check node processor complexity and the decoder memory requirements. Float-point and fixed-point simulation results show that a near optimum performance can be maintained. The architecture of a check node processor implementing the partial-min algorithms is also presented. The hardware expense especially the memory requirement is analyzed and compared with normal decoding architectures