Universal Fixed-Length Coding Redundancy

We consider the problem of choosing a block-length to achieve a desired probability of error for fixed-length lossless source coding and channel coding of a finite amount of payload data. This is closely related to the issue of redundancy. While Baron, et al. studied this problem for rates in the vicinity of entropy for known source distributions and for rates in the vicinity of capacity for known channels using central-limit-theorem style asymptotics, we are interested in all rates for unknown source distributions and unknown channels. By using the universal lower bound on the source coding error exponents and the similar universal lower-bound to the channel coding error exponent, we derive universal upper bounds to the redundancy rate that are non-asymptotic in that they are explicitly valid for all alphabet sizes, all block lengths, and all target error probabilities. Because of the simplicity of the bounds, they also shed light on the large alphabet asymptotics for both source and channel coding.