Abstract
For a given arbitrary list of integer numbers, in general there is no known single universal code which is an overall optimum in the sense of representing the whole list with the shortest average codeword length. This is the motivation in this paper to introduce a class of adaptive universal codes based on pattern codes, for integer representation. A construction of adaptive universal codes is given, which is based on Fibonacci codes. This construction is shown to perform well over a wider range of integer values in comparison to known universal code constructions.
Highlights
For a given arbitrary list of integer numbers, in general there is no known single universal code which is an overall optimum in the sense of representing the whole list with the shortest average codeword length [1], [8], [9], [17], where by the length of a codeword we mean the number of digits that it contains
We were motivated to try an alternative approach and partially circumvent this difficulty by introducing adaptive universal (AU) [18] codes based on pattern codes, originally treated as prefix codes by Gilbert [3]
When considering a sufficiently large range of integers, the integer representation provided by a single Fibonacci code is not uniformly better than that given by another Fibonacci code
Summary
HE efficient encoding and decoding of an arbitrary list of integer numbers, often in a compact representation [1], [2], represents an interesting problem in areas such as source coding theory [3]-[6], data compression [7]-[10], digital data transmission theory [11], [12], synchronizable codes [11],. According to Capocelli [14], for a given positive integer r, universal codes can be constructed by considering the set of all binary strings of length greater than or equal to r in which the sequence formed by a 0 followed by r − 1 1’s, denoted as 01r−1 , occurs only once as a suffix. These binary strings form a countably infinite set of prefix-free codewords which we will denote by S = S(r, 01r−1 ).
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