Lossless Data Compression via Substring Enumerationのマルコフ情報源に対する最悪冗長度

摘要

DubeとBeaudoinはCompression via Substring Enumeration(CSE)と呼ばれるユニバーサル無歪みデータ圧縮法を2010年に提案した.本稿では，k次マルコフ情報源からの任意の個別系列に対してCSE符号化を行った 場合の冗長度の上界について評価する.その結果，CSEの個別最悪冗長度とクラフトの不等式を満たす最適な固定長-可変長符号で達成可能な最悪冗長度の差は，符号化する系列長nに対して，高々log n程度であることを明らかにする.%Dube and Beaudoin proposed a technique of lossless data compression called compression via substring enumeration (CSE) in 2010. This paper evaluates an upper bound of the amount of bits used by the CSE technique to encode any individual string from an unknown member of a known class of fc-th order Markov processes. We compare the worst case maximum redundancy obtained by the CSE technique for any binary string with the least possible value of the worst case maximum redundancy obtained by the best fixed-to-variable length code satisfying the Kraft inequality. We clarify that the difference of the worst case maximum redundancies is at most log n+constant, where n denotes the length of a binary string to be encoded.