Second-order capacities of erasure and list decoding

We derive the second-order capacities (supremum of second-order coding rates) for erasure and list decoding. Fpor erasure decoding, we show that second-order capacity is √VΦ^-1(ε_t) where V is the channel dispersion and (ε_t is the total error probability, i.e. the sum of the erasure and undetected errors. We show numerically that the expected rate at finite blocklength for erasures decoding can exceed the finite blocklength channel coding rate. For list decoding, we consider list codes of deterministic size 2^√nl and show that the second-order capacity is l+ √VΦ^-1(ε) where ε is the permissible error probability. Both coding schemes use the threshold decoder and converses are proved using variants of the meta-converse.