Results 1  10
of
37
A general framework for codes involving redundancy minimization
 IEEE Transactions on Information Theory
, 2006
"... Abstract — A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework involves a twoparameter class encompassing problems previously proposed by Huffman [1], Campbell [2], Nath [3], and Drmota and Szpankowsk ..."
Abstract

Cited by 9 (6 self)
 Add to MetaCart
(Show Context)
Abstract — A framework with two scalar parameters is introduced for various problems of finding a prefix code minimizing a coding penalty function. The framework involves a twoparameter class encompassing problems previously proposed by Huffman [1], Campbell [2], Nath [3], and Drmota and Szpankowski [4]. It sheds light on the relationships among these problems. In particular, Nath’s problem can be seen as bridging that of Huffman with that of Drmota and Szpankowski. This leads to a lineartime algorithm for the last of these with a solution that solves a range of Nath subproblems. We find simple bounds and lineartime Huffmanlike optimization algorithms for all nontrivial problems within the class.
Precise asymptotic analysis of the Tunstall code
 Proc. 2006 International Symposium on Information Theory (Seattle
"... A variabletofixed length encoder partitions the source string over an mary alphabet A into a concatenation of variablelength phrases. Each phrase except the last one is constrained to belong to a given dictionary D of source strings; the last phrase is a nonnull prefix of a dictionary entry. On ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
A variabletofixed length encoder partitions the source string over an mary alphabet A into a concatenation of variablelength phrases. Each phrase except the last one is constrained to belong to a given dictionary D of source strings; the last phrase is a nonnull prefix of a dictionary entry. One common constraint on a dictionary is that it leads to a unique parsing of any string over A. We will assume that all dictionaries are uniquely parsable. It is convenient to represent a uniquely parsable dictionary by a complete parsing tree T, i.e., a tree in which every internal node has all m children nodes in the tree. The dictionary entries d ∈Dcorrespond to the leaves of parsing tree. The encoder represents each parsed string by the fixed length binary code word corresponding to its dictionary entry. If the dictionary D is has M entries, then the code word for each phrase has
The minimum average code for finite memoryless monotone sources
 in Proc., IEEE Information Theory Workshop
, 2002
"... Abstract—The problem of selecting a code for finite monotone sources with x symbols is considered. The selection criterion is based on minimizing the average redundancy (called Minave criterion) instead of its maximum (i.e., Minimax criterion). The average probability distribution € x, whose associa ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract—The problem of selecting a code for finite monotone sources with x symbols is considered. The selection criterion is based on minimizing the average redundancy (called Minave criterion) instead of its maximum (i.e., Minimax criterion). The average probability distribution € x, whose associated Huffman code has the minimum average redundancy, is derived. The entropy of the average distribution (i.e.,
Minimum Expected Length of FixedtoVariable Lossless Compression of Memoryless Sources
"... Abstract—Conventional wisdom states that the minimum expected length for fixedtovariable length encoding of an nblock memoryless source with entropy H grows as nH+O(1). However, this performance is obtained under the constraint that the code assigned to the whole nblock is a prefix code. Droppin ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract—Conventional wisdom states that the minimum expected length for fixedtovariable length encoding of an nblock memoryless source with entropy H grows as nH+O(1). However, this performance is obtained under the constraint that the code assigned to the whole nblock is a prefix code. Dropping this unnecessary constraint we show that the minimum expected length grows as nH − 1 log n + O(1) 2 unless the source is equiprobable. I.
Optimal prefix codes for infinite alphabets with nonlinear costs
 IEEE Trans. Inf. Theory
, 2008
"... Abstract — Let P = {p(i)} be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial P for which known methods find a source code that is optimal in the sense of minimizing ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Abstract — Let P = {p(i)} be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial P for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective P functions, βexponential means, those of the form loga i p(i)an(i) , where n(i) is the length of the ith codeword and a is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in singleshot communications (a < 1) and a previously known problem of minimizing the chance of buffer overflow in a queueing system (a> 1). This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered. Index Terms — Communication networks, generalized entropies, generalized means, Golomb codes, Huffman algorithm,
Tunstall Code, Khodak Variations, and random Walks
, 2008
"... A variabletofixed length encoder partitions the source string into variablelength phrases that belong to a given and fixed dictionary. Tunstall, and independently Khodak, designed variabletofixed length codes for memoryless sources that are optimal under certain constraints. In this paper, we s ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
A variabletofixed length encoder partitions the source string into variablelength phrases that belong to a given and fixed dictionary. Tunstall, and independently Khodak, designed variabletofixed length codes for memoryless sources that are optimal under certain constraints. In this paper, we study the Tunstall and Khodak codes using analytic information theory, i.e., the machinery from the analysis of algorithms literature. After proposing an algebraic characterization of the Tunstall and Khodak codes, we present new results on the variance and a central limit theorem for dictionary phrase lengths. This analysis also provides a new argument for obtaining asymptotic results about the mean dictionary phrase length and average redundancy rates.
Tight bounds on minimum maximum pointwise redundancy
 In Proceedings of the International Symposium on Information Theory
, 1944
"... Abstract — This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of minimizing maximum pointwise redundancy. This objective re ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract — This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of minimizing maximum pointwise redundancy. This objective relates to both universal modeling and Shannon coding, and these bounds are tight throughout the interval. The upper bounds also apply to a related objective, that of d th exponential redundancy. I.
A New Algorithm for Building Alphabetic Minimax Trees
, 2008
"... We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample. ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample.
Benefiting from disorder: Source coding for unordered data. arXiv
, 708
"... The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding, universal lossless coding, ratedistortion, highrate quantization, ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding, universal lossless coding, ratedistortion, highrate quantization, and universal lossy coding. The main conclusions demonstrate that there is a significant rate savings when order is irrelevant. In particular, lossless coding of n letters from a finite alphabet requires Θ(log n) bits and universal lossless coding requires n + o(n) bits for many countable alphabet sources. However, there are no universal schemes that can drive a strong redundancy measure to zero. Results for lossy coding include distributionfree expressions for the rate savings from order irrelevance in various highrate quantization schemes. Ratedistortion bounds are given, and it is shown that the analogue of the Shannon lower bound is loose at all finite rates.