Decoding Error Probability of the Random Matrix Ensemble over the Erasure Channel
Abstract
Using tools developed in a recent work by Shen and the second author, in this paper we carry out an indepth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random matrix ensemble and the error exponent of the variance, which imply a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.09989
 Bibcode:
 2021arXiv210809989H
 Keywords:

 Computer Science  Information Theory;
 94A40;
 94B70
 EPrint:
 4 figures