Efficient Coding of Integers for Certain Probability Distributions

Methods for prefix coding integers generally either consider specific distributions that decline more quickly than a power law (for Golomb-like codes) or simultaneously consider all finite-entropy distributions (for universal codes). Particular power-law and similar distributions, however, are often known to model particular random variables. Codes for such distributions can be judged based on (estimated) compression ratio. This paper introduces a family of universal source codes with an eye towards near-optimal coding of known distributions. Compression ratios are found for well-known probability distributions using these codes and other prefix codes. One application of these nearoptimal codes is an improved representation of rational numbers.