Abstract
This paper proposes a unified framework to describe the check node architectures of non-binary low-density parity-check (NB-LDPC) decoders. Forward-backward, syndrome-based, and pre-sorting approaches are first described. Then, they are hybridized in an effective way to reduce the amount of computation required to perform a check node. This paper is specially impacting check nodes of high degrees (or high coding rates). Results of 28-nm ASIC post-synthesis for a check node of degree 12 (i.e., a code rate of 5/6 with a degree of variable equal to 2) are provided for NB-LDPC over GF(64) and GF(256). While simulations show almost no performance loss, the new proposed hybrid implementation check node increases the hardware and the power efficiency by a factor of six compared with the classical forward-backward architecture. This leads to the first ever reported implementation of a degree 12 check node over GF(256), and these preliminary results open the road to high decoding throughput, high rate, and high-order Galois field NB-LDPC decoder with a reasonable hardware complexity.
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