Related papers: The length of a typical Huffman codeword
We compare an efficiency of a deterministic "lawnmower" and random search strategies for finding a prescribed sequence of letters (a password) of length M in which all letters are taken from the same Q-ary alphabet. We show that at best a…
This paper describes a new set of block source codes well suited for data compression. These codes are defined by sets of productions rules of the form a.l->b, where a in A represents a value from the source alphabet A and l, b are -small-…
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…
Word complexity is defined in a number of different ways. Psycholinguistic, morphological and lexical proxies are often used. Human ratings are also used. The problem here is that these proxies do not measure complexity directly, and human…
Huffman coding finds an optimal prefix code for a given probability mass function. Consider situations in which one wishes to find an optimal code with the restriction that all codewords have lengths that lie in a user-specified set of…
Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…
The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are…
Given uniform probability on words of length M=Np+k, from an alphabet of size p, consider the probability that a word (i) contains a subsequence of letters (p, p-1,...,1) in that order and (ii) that the maximal length of the disjoint union…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
Lossless variable-length source coding with unequal cost function is considered for general sources. In this problem, the codeword cost instead of codeword length is important. The infimum of average codeword cost has already been…
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
In this paper we consider the class of anti-uniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions…
In this paper we consider lossless source coding for a class of sources specified by the total variational distance ball centred at a fixed nominal probability distribution. The objective is to find a minimax average length source code,…
We investigate two source coding problems with secrecy constraints. In the first problem we consider real--time fully secure transmission of a memoryless source. We show that although classical variable--rate coding is not an option since…
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…
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
For every fixed finite field $\F_q$, $p \in (0,1-1/q)$ and $\epsilon > 0$, we prove that with high probability a random subspace $C$ of $\F_q^n$ of dimension $(1-H_q(p)-\epsilon)n$ has the property that every Hamming ball of radius $pn$ has…
For some applications where the speed of decoding and the fault tolerance are important, like in video storing, one of the successful answers is Fix-Free Codes. These codes have been applied in some standards like H.263+ and MPEG-4. The…