  Using tools developed in a recent work by Shen and the second author, in this
paper we carry out an in-depth 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.
