---
title: Prefix Codes for Power Laws with Countable Support
url: https://www.emergentmind.com/papers/0611073
type: paper
arxiv_id: '0611073'
arxiv_url: https://arxiv.org/abs/0611073
published: '2006-11-15'
categories:
- cs.IT
- math.IT
---

# Prefix Codes for Power Laws with Countable Support

## Abstract

In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many random variables encountered in practice. For such random variables, compression performance is judged via estimates of expected bits per input symbol. This correspondence introduces a family of prefix codes with an eye towards near-optimal coding of known distributions. Compression performance is precisely estimated for well-known probability distributions using these codes and using previously known prefix codes. One application of these near-optimal codes is an improved representation of rational numbers.