Error-and-Erasure Decoding for Block Codes with Feedback

Abstract: Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with communication and control phases together with the optimal decoding rule for the given encoding scheme, among decoding rules that can be represented in terms of pairwise comparisons between the messages. Then an outer bound is derived using a generalization of the straight-line bound to errors-and-erasures decoders and the optimal error exponent trade off of a feedback encoder with two messages. In addition upper and lower bounds are derived, for the optimal erasure exponent of error free block codes in terms of the rate. Finally we present a proof of the fact that the optimal trade off between error exponents of a two message code does not increase with feedback on DMCs.