Error-Free Communication Over State-Dependent Channels with Variable-Length Feedback

摘要

The zero-error capacity of state-dependent channels with noiseless feedbackis determined, under the assumption that the transmitter and the receiver areallowed to use variable-length coding schemes. Various cases are analyzed, withthe employed coding schemes having either bounded or unbounded codeword lengthsand with state information revealed to the encoder and/or decoder in a strictlycausal, causal, or non-causal manner. In each of these settings, necessary andsufficient conditions for positivity of the zero-error capacity are obtainedand it is shown that, whenever the zero-error capacity is positive, it equalsthe conventional vanishing-error capacity. Moreover, it is shown that thevanishing-error capacity of state-dependent channels is not increased by theuse of feedback and variable-length coding. A comparison of the results withthe recently solved fixed-length case is also given.