On the influence of erasure correction on the probability of undetected error of Reed-Solomon codes

This paper analyzes several aspects of erasure correction in the decoding of Reed-Solomon (RS) codes over the q-ary Erasure Channel. It is shown that by limiting the maximum number of erasures the decoder is allowed to correct, a significant improvement in the probability of undetected error is obtained, at relatively high channel erasure and low channel transition probabilities. Of particular interest is the errata pattern with the maximum number of erasures the RS code can correct and at least one error, which always causes an undetected error in an incomplete decoder. This "limited erasures" approach is compared with the "readable erasures" method. This approach is also analyzed for concatenated codes using an RS code as the outer code.