Reduced-Complexity Multiplicity Assignment Algorithm and Architecture for Low-Complexity Chase Decoder of Reed-Solomon Codes

A reduced-complexity multiplicity assignment (RCMA) algorithm for low-complexity chase (LCC) is proposed for decoding Reed-Solomon (RS) codes. The properties of bit-level received voltages over an additive white Gaussian noise (AWGN) channel with binary modulation are explored. By using the properties, the hard-decision, secondary hard-decision, and unreliable positions can be easily determined, and hence, significantly reduce the computational complexity. Compared with the original multiplicity assignment (MA) algorithm, the RCMA eliminates n
²
log
²
n multiplication operations and reduces the number of comparison operations from 2n
²
to n log
²
n, where n is the code length of an RS code. Moreover, a hardware design for RCMA is proposed and applied in the unified syndrome computation (USC) based LCC decoder. Implementation results show the throughput of the proposed decoder can reach a Gbps order, which meets the requirements of high-speed communications.