Takahiro Ota

On the adaptive antidictionary code using minimal forbidden words with constant lengths

This paper proposes a new on-line antidictionary code with linear time. The proposed algorithm uses a subset of antidictionary which length of the elements is at most a given fixed length. It is proved that the time complexity of this algorithm is linear with respect to the string length. Its effectiveness is demonstrated by simulation results.

On the On-line Arithmetic Coding Based on Antidictionaries with Linear Complexity

This paper proposes an on-line data compression based on antidictionaries with linear time. The proposed algorithm works using only suffix trees without constructing of antidictionaries, and we prove that the time complexity of this algorithm is linear with respect to the string length. Furthermore, the proposed algorithm produces the tree model based on antidictionaries. This tree model gives an efficient probabilistic model for entropy codings. Its effectiveness is demonstrated by simulation results.

On antidictionary coding based on compacted substring automaton

Lossless data compression via substring enumeration (CSE) has been proposed by Dubé and Beaudoin in 2010. The CSE outputs its encoder called compacted substring automaton as a codeword, and an efficient representation of the automaton is also proposed. In this paper, we prove an isomorphism between compacted substring automaton and antidictionary automaton, which is an encoder of antidictionary coding. Then we propose a new static antidictionary coding which uses the representation of compacted substring automaton instead of antidictionary. Moreover, we prove an asymptotic optimality of the proposed coding for a stationary ergodic source.

On the Construction of an Antidictionary with Linear Complexity Using the Suffix Tree

The antidictionary of a string is the set of all words of minimal length that never appear in this string. Antidictionaries are in particular useful for source coding. We present a fast and memory-efficient algorithm to construct an antidictionary using a suffix tree. It is proved that the complexity of this algorithm is linear in space and time, and its effectiveness is demonstrated by simulation results.

On fast and memory-efficient construction of an antidictionary array

An antidictionary, a set of words that never appear in a given string, is a useful data structure for source coding as well as other fields of computer sciences. A fast and memory-efficient algorithm for constructing antidictionaries by means of suffix array is presented. We prove that the proposed algorithm constructs an antidictionary array with linear time and space.

Asymptotic optimality of antidictionary codes

An antidictionary code is a lossless compression algorithm using an antidictionary which is a set of minimal words that do not occur as substrings in an input string. The code was proposed by Crochemore et al. in 2000, and its asymptotic optimality has been proved with respect to only a specific information source, called balanced binary source that is a binary Markov source in which a state transition occurs with probability 1/2 or 1. In this paper, we prove the optimality of both static and dynamic antidictionary codes with respect to a stationary ergodic Markov source on finite alphabet such that a state transition occurs with probability p (0 < p ≤ 1).

Length of minimal forbidden words on a stationary ergodic source

An antidictionary is in particular useful for data compression, and it consists of minimal forbidden words for a given string. We derive the average length Mn of minimal forbidden words in strings of length n under a stationary ergodic source with entropy H which takes values on a finite alphabet. For the string length n, we prove, log n/Mn = H, in probability, as n ↑ ∞. We use the Wyner-Ziv result, with respect to connection between entropy and recurrence-time for ergodic processes, to prove the theorem. Its validity is shown by simulation results on a memoryless binary information source.

On the sliding window variations of antidictionary data compression using dynamic suffix trees

Two sliding window variations of an adaptive arithmetic coding method based on dynamic antidictionaries of the input data are proposed. Due to a limited size of sliding window, the proposed methods are memory-efficient and suitable for handling an extremely long string in constant space. Moreover, one of the proposed methods works in linear time with respect to the string length. It is shown that the proposed methods achieve better compression ratios than the traditional compression coding methods by simulation results.

Dynamic construction of an antidictionary with linear complexity

An antidictionary is in particular useful for data compression. Static construction algorithms of antidictionaries with linear complexity have been proposed. However, the construction algorithms do not work in a dynamic manner with linear complexity. In this paper, we propose a dynamic construction algorithm of an antidictionary with linear complexity. The proposed algorithm uses two linear construction algorithms of suffix trees proposed by Weiner and Ukkonen, individually. It is proved that the proposed algorithm works with linear complexity. Moreover, its effectiveness is demonstrated by simulation results.

On the dynamic construction of an antidictionary with linear complexity

An antidictionary is in particular useful for data compression. Static construction algorithms of antidictionaries with linear complexity have been proposed. However, the construction algorithms do not work in a dynamic manner with linear complexity. In this paper, we propose a dynamic construction algorithm of an antidictionary with linear complexity. The proposed algorithm uses two linear construction algorithms of suffix trees proposed by Weiner and Ukkonen, individually. It is proved that the proposed algorithm works with linear complexity. Moreover, its effectiveness is demonstrated by simulation results.