Second order asymptotics in fixed-length source coding and intrinsic randomness

TL;DR

This paper explores the second order asymptotics of fixed-length source coding and intrinsic randomness, revealing differences in optimal rates and establishing a universal code for general sources.

Contribution

It introduces the second order asymptotics analysis for source coding and intrinsic randomness, highlighting differences in optimal rates and constructing a universal code.

Findings

Optimal rates differ between source coding and intrinsic randomness in second order asymptotics.

The results apply to general sources, including i.i.d. distributions.

A universal code achieving second order optimality is constructed.

Abstract

Second order asymptotics of fixed-length source coding and intrinsic randomness is discussed with a constant error constraint. There was a difference between optimal rates of fixed-length source coding and intrinsic randomness, which never occurred in the first order asymptotics. In addition, the relation between uniform distribution and compressed data is discussed based on this fact. These results are valid for general information sources as well as independent and identical distributions. A universal code attaining the second order optimal rate is also constructed.