Errors-and-Erasures Decoding for Block Codes With Feedback

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 tradeoff 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, a proof is provided for the fact that the optimal tradeoff between error exponents of a two-message code does not improve with feedback on discrete memoryless channels (DMCs).