The minimum achievable redundancy rate of fixed-to-fixed length source codes for general sources

Abstract

This paper investigates the minimum achievable redundancy rate of fixed-to-fixed length lossless source codes (FF codes) for general sources. This paper defines the redundancy rate of the FF code by the difference between the coding rate and the self information rate. We prove that the minimum achievable redundancy rate is equal to the limit superior in probability of the width of the information spectrum, which is defined in this paper. This paper also considers the e-source coding. We show two criteria for bounding the error probability. The first one bounds the sum of the decoding error probability and the redundancy-overflow probability, and the other one bounds these two probabilities separately. We also give the minimum achievable redundancy rate of these two types of e-source coding.