An Efficient Fully Parallel Decoder Architecture for Nonbinary LDPC Codes

Nonbinary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in some cases, but their high decoding complexity is a significant hurdle to their applications. In this paper, we propose a decoding algorithm with reduced computational complexities and smaller memory requirements for NB-LDPC codes. First, a simplified algorithm is proposed to reduce the computational complexity of variable node processing. To reduce the memory requirements, existing NB-LDPC decoders often truncate the message vectors to a limited number n_m of values. However, the memory requirements of these decoders remain high when the field size is large. In this paper, an improved trellis-based check node processing algorithm is proposed to significantly reduce the memory requirement. The number of elements in a variable-to-check message is reduced to n_v (n_v <; n_m). The sorted log likelihood ratio (LLR) vector of a check-to-variable (c-to-v) message is approximated using a piecewise linear function. For each a priori message, most of the LLRs are approximated with a linear function. Two low complexity LLR generation units (LGUs) are proposed to compute LLR vectors for c-to-v messages. A fully parallel NB-LDPC decoder over GF(256) is implemented with 28-nm CMOS technology. The decoder over GF(256) achieves a throughput of 546 Mb/s and an energy efficiency of 0.178 nJ/b/iter.