Erasure correction performance of linear block codes

Abstract

We estimate the probability of incorrect decoding of a linear block code, used over an erasure channel, via its weight spectrum, and define the weight spectra that allow us to achieve the capacity of the channel and the random coding exponent. We derive the erasure correcting capacity of long binary BCH codes with slowly growing distance and their duals. Concatenated codes of growing length n→∞ and polynomial decoding complexity O(n²), achieving the capacity of the erasure channel (or any other discrete memoryless channel), are considered.