Two-dimensional source coding by means of subblock enumeration

Abstract

Abstract-. It is reported that performance of the CSE [4] is as well as that of an efficient off-line data compression algorithm using the Burrows-Wheeler transformation (BWT) [6]. In [7], it is proved that an encoder, which is a deterministic finite automaton, of the CSE and an encoder without sinks of the antidictionary coding [8] are isomorphic for a binary source. Moreover, an antidictionary coding proposed in [9] provided the first CSE for q-ary (q > 2) alphabet sources as a byproduct. Iwata and Arimura proposed the modified algorithm and evaluated the maximum redundancy rate of the CSE for the kth order Markov sources [10].For encoding an input source, the CSE utilizes a probabilistic model built from the circular string which is obtained by concatenating the first symbol to the last symbol of the source. A probabilistic model of the circular string is also useful for the BWT and antidictionary coding [7], [9], and in [11], it is shown that an antidictionary built from the circular string is useful for genome comparison such as deoxyribonucleic acid (DNA). However, for a 2D source such as an image, computational time of the CSE is exponential with respect to line length since the CSE works in line-by-line. The CSE deals

A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration

“…As for 0 ( p), from the assumption and m ≤ n, we have 0 ( p) ≤ 2(2 log 2 n + 1) + log 2 mn , where (2 log 2 n + 1) and log 2 mn are the costs of the Elias code for integers n and (rank( p)), respectively. As for 1 ( p), the cost of N (b i ) in Condition (P-i) is log 2 mn bits from (18), so that 1 ( p) ≤ (|X| − 1) log 2 mn . As for 2 ( p), since I (b i ) ≤ mn and I (b i ) ≤ mn, the costs of I (b i ) and I (b i ) are at most log 2 mn bits.…”

“…* This paper was presented in part at the IEEE International Symposium on Information Theory, Aachen, Germany, July 2017 [18].…”