Redundancy-Optimal FF Codes for a General Source and Its Relationships to the Rate-Optimal FF Codes

Mitsuharu ARIMURA  Hiroki KOGA  Ken-ichi IWATA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.12   pp.2332-2342
Publication Date: 2013/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.2332
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Source Coding
fixed-to-fixed length source coding,  information-spectrum methods,  general sources,  coding rate,  redundancy,  

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In this paper we consider fixed-to-fixed length (FF) coding of a general source X with vanishing error probability and define two kinds of optimalities with respect to the coding rate and the redundancy, where the redundancy is defined as the difference between the coding rate and the symbolwise ideal codeword length. We first show that the infimum achievable redundancy coincides with the asymptotic width W(X) of the entropy spectrum. Next, we consider the two sets $mCH(X)$ and $mCW(X)$ and investigate relationships between them, where $mCH(X)$ and $mCW(X)$ denote the sets of all the optimal FF codes with respect to the coding rate and the redundancy, respectively. We give two necessary and sufficient conditions corresponding to $mCH(X) subseteq mCW(X)$ and $mCW(X) subseteq mCH(X)$, respectively. We can also show the existence of an FF code that is optimal with respect to both the redundancy and the coding rate.