Average error exponent of undetected error probability of binary matrix ensembles

We evaluate average error exponent of the undetected error probability of binary matrix ensembles by applying statistical-mechanics approach, which is called the “quenched” average error exponent. In the exixting analysis, the “annealed” average error exponent, which is the error exponent of the average undetected error probability, has been evaluated. The quenched average error exponent is more suitable to capture typical behaviors. We show that there are some cases where the annealed exponent is overestimated for the irregular sparse matrix ensemble. We also show that the quenched average error exponent is equivalent to the annealed average error exponents for the regular sparse matrix ensemble.