Explicit Formulas and Error Exponents for Decoding Error Probability of Random Parity-Check Matrix Ensemble over the Erasure Channel

The authors derive explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under unambiguous decoding, maximum likelihood decoding, and list decoding over the erasure channel. They also compute the error exponents of these average decoding error probabilities and establish a strong concentration result for the unsuccessful decoding probability under unambiguous decoding.