This paper presents a modified Trellis Min-Max (T-MM) algorithm together with the associated architecture for non-binary (NB) low-density parity-check (LDPC) decoders. The proposed T-MM algorithm is able to reduce the memory requirements for the check-node messages through an efficient compression method and enhance the error-rate performance using the appropriate decompression. A method of updating the a posteriori log-likelihood ratio in the delta domain is used to simplify the computational and storage complexity. In order to enhance the decoding throughput, a low-complexity early termination (ET) scheme is devised by using the hard decisions of the variable-to-check messages, where, although a minor overhead is introduced, there is no visible degradation in error rate. As a proof of concept, a row-parallel layered decoder for the 32-ary (837, 726) LDPC code is implemented using a 90-nm CMOS process. The proposed decoder achieves a throughput of 1.64 Gb/s at 526.32 MHz based on eight iterations and has an area of 6.86 mm 2. When the ET scheme is enabled, the decoder achieves a maximum throughput of 4.68 Gb/s with a frame error rate of 3.25 × 10 −6 at E b /N 0 = 4.5 dB. The proposed NB-LDPC decoder achieves the highest throughput and hardware efficiency compared to the state-of-the-art decoders, even when the ET scheme is not enabled. INDEX TERMS Non-binary low-density parity-check (NB-LDPC) codes, trellis min-max (T-MM) algorithm, layered decoding, early termination (ET), high-throughput decoder, very large scale integration (VLSI) architecture. YEONG-LUH UENG (M'05-SM'15) received the Ph.D. degree in communication engineering from
This paper presents an efficient min-sum-based decoder for high-rate low-density parity-check (LDPC) codes, where the first minimum and second minimum values are stored in registers. In order to meet a strict cost requirement imposed by NAND flash applications, we provide different upper limits for the first and second minimum values. Furthermore, we use non-uniform quantization for the second minimum value so as to reduce storage complexity. In order to enhance the errorrate performance, the normalization factor is determined based on the difference between the first two minimum values. Using the proposed techniques, a reduction in gate count of 13.36% can be achieved without suffering any degradation in errorrate performance. The implementation results for a rate-0.896 length-18624 layered decoder show that this decoder can achieve a throughput of 765.24 Mb/s at a clock frequency of 166 MHz with a gate count of 620K.
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