Variable-length channel codes with probabilistic delay guarantees

Variable-length channel codes over discrete memoryless channels subject to probabilistic delay guarantees are examined in the non-vanishing error probability regime. Fundamental limits of these codes in several different settings, which depend on the availability of noiseless feedback and a termination option, are investigated. In stark contrast with average delay guarantees, the first-order terms of the fundamental limits turn out to be the same as those for fixed-length codes in all cases. Further, feedback is shown to improve the second-order term, even in the absence of a termination option.