On calculating interpolation polynomials for error values in Reed-Solomon decoding algorithm

Abstract

Systematic ways of generating interpolation polynomials for error values in parallel Reed-Solomon decoding were discussed. It was found that the coefficients could be calculated in a closed form with as low as O(t2) multiplications. Simulation results showed that a single decoder with the decoding algorithm could achieve a throughput of more than 40 Gbps assuming a 0.18-μm CMOS technology by avoiding costly symbol-by-symbol divisions in calculating error values.