The Decoding Error Probability of Linear Codes Over the Erasure Channel
Linzhi Shen, Fang‐Wei Fu · IEEE Transactions on Information Theory · 2019
In this paper, we study the decoding error probability of linear codes over the erasure channel under the list decoding. The notion of the qℓ-incorrigible sets of linear codes is introduced to characterize its decoding error probability under the list decoding or the maximum likelihood decoding. By calculating the qℓ-incorrigible set distributions, the decoding error probability of a linear code over the erasure channel under the list decoding or the maximum likelihood decoding is expressed by its support weight distributions. For the ensemble of all [n,k] linear codes, the average decoding error probability under the maximum likelihood decoding and the average unsuccessful decoding probability under unambiguous decoding are determined. Furthermore, the error exponent of the average unsuccessful decoding probability under the unambiguous decoding is determined for the ensemble of all [n,nR] linear codes.