Achievable Error Exponents for Channel with Side Information - Erasure and List Decoding

Abstract: We consider a decoder with an erasure option and a variable size list decoder for channels with non-casual side information at the transmitter. First, universally achievable error exponents are offered for decoding with an erasure option using a parameterized decoder in the spirit of Csisz\'{a}r and K\"{o}rner's decoder. Then, the proposed decoding rule is generalized by extending the range of its parameters to allow variable size list decoding. This extension gives a unified treatment for erasure/list decoding. Exponential bounds on the probability of list error and the average number of incorrect messages on the list are given. Relations to Forney's and Csisz\'{a}r and K\"{o}rner's decoders for discrete memoryless channel are discussed. These results are obtained by exploring a random binning code with conditionally constant composition codewords proposed by Moulin and Wang, but with a different decoding rule.