Analysis of Bounded Distance Decoding for Reed Solomon Codes

Bounded distance decoding of Reed-Solomon codes involves finding a unique codeword if there is at least one codeword within the given distance. A corrupted message having errors that is less than or equal to half the minimum distance corresponds to a unique codeword and therefore, the probability of decoding error is one for a minimum distance decoder. However, increasing the decoding radius to be slightly higher than half of the minimum distance may result in multiple codewords within the Hamming sphere. In this study, we computed the probability of having unique codewords for (7,k) RS codes when the decoding radius is increased from the error correcting capability t to t+1. Simulation results show a significant effect of the code rates on the probability of having unique codewords. It also shows that the probability of having unique codeword for low rate codes is close to one.