Universal Quadratic Lower Bounds on Source Coding Error Exponents

We consider the problem of block-size selection to achieve a desired probability of error for universal source coding. While Baron, et al. (2004; 1973) studied this question for rates in the vicinity of entropy for known distributions using central-limit-theorem techniques, we are interested in all rates for unknown distributions and use error-exponent techniques. By adapting a technique of Gallager from the exercises of Gallager (1971), we derive a universal lower bound to the source-coding error exponent that depends only on the alphabet size and is quadratic in the gap to entropy.