Prefix Codes: Equiprobable Words, Unequal Letter Costs

Describes a near-linear-time algorithm for a variant of Huffman coding, in which the letters may have non-uniform lengths (as in Morse code), but with the restriction that each word to be encoded has equal probability. [See also ``Huffman Coding with Unequal Letter Costs'' (2002).]Comment: proceedings version in ICALP (1994

Infinite anti-uniform sources

6 pagesInternational audienceIn this paper we consider the class of anti-uniform Huffman (AUH) codes for sources with infinite alphabet. Poisson, negative binomial, geometric and exponential distributions lead to infinite anti-uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as a result of this encoding, we obtain sources with memory. For these sources we attach the graph and derive the transition matrix between states, the state probabilities and the entropy. If c0 and c1 denote the costs for storing or transmission of symbols "0" and "1", respectively, we compute the average cost for these AUH codes

More Efficient Algorithms and Analyses for Unequal Letter Cost Prefix-Free Coding

There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are many good heuristics that all provide additive errors to optimal. The additive error in these algorithms usually depends linearly upon the largest encoding letter size. This paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite. Because the largest letter cost is infinite, the previous analyses could give infinite error bounds. We provide a new algorithm that works with infinite encoding alphabets. When restricted to the finite alphabet case, our algorithm often provides better error bounds than the best previous ones known.Comment: 29 pages;9 figures

Optimal Variable Length Codes (Arbitrary Symbol Cost and Equal Code Word Probability)

The problem of constructing minimum-redundancy prefix codes for the general discrete noiseless channel without constraints is solved for unequal code letter costs, provided that the symbols encoded are assumed to be equally probable. A graphical technique is developed for solving the problem for which the code words are equally probable and are constructed from r symbols where r is greater than or equal to two. A method is given for constructing an optimal exhaustive prefix code. This method is then generalized to the extent that the exhaustive constraint is deleted, thereby resulting in an algorithm, designated ACE for arbitrary symbol cost and equal code word probability, which solves the stated problem. Abstract © Elsevie

Huffman Coding with Letter Costs: A Linear-Time Approximation Scheme

We give a polynomial-time approximation scheme for the generalization of Huffman Coding in which codeword letters have non-uniform costs (as in Morse code, where the dash is twice as long as the dot). The algorithm computes a (1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is the input size

New Classes of Random Sequences for Coding and Cryptography Applications

Cryptography is required for securing data in a digital or analog medium and there exists a variety of protocols to encode the data and decrypt them without third party interference. Random numbers must be used to generate keys so that they cannot be guessed easily. This thesis investigates new classes of random numbers, including Gopala-Hemachandra (GH) and Narayana sequences, which are variants of the well-known Fibonacci sequences. Various mathematical properties of GH and Narayana sequences modulo prime have been found including their periods. Considering GH sequences modulo prime p, the periods are shown to be either (p-1) (or a divisor) or (2p+2) (or a divisor) while the Narayana sequence for prime modulo have either p2+p+1 (or a divisor) or p2-1 (or a divisor) as their periods. New results on the use of the Narayana sequence as a universal code have been obtained.It is shown that the autocorrelation and cross correlation properties of GH and Narayana sequences justify their use as random sequences. The signal to noise ratio values are calculated based on the use of delayed sequences to carry different sets of data in wireless applications. The thesis shows that GH and Narayana sequences are suitable for many encoding and decoding applications including key generation and securing transmission of data.Electrical Engineerin