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Dynamic Shannon Coding
, 2005
"... We present a new algorithm for dynamic prefixfree coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient lengthr ..."
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Cited by 9 (7 self)
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We present a new algorithm for dynamic prefixfree coding, based on Shannon coding. We give a simple analysis and prove a better upper bound on the length of the encoding produced than the corresponding bound for dynamic Huffman coding. We show how our algorithm can be modified for efficient lengthrestricted coding, alphabetic coding and coding with unequal letter costs.
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 ..."
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Cited by 9 (6 self)
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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.
Analytic Variations on Redundancy Rates of Renewal Processes
 IEEE Trans. Information Theory
, 2002
"... Csisz ar and Shields have recently proved that the minimax redundancy for a class of (stationary) renewal processes is ( n) where n is the block length. This interesting result provides a first nontrivial bound on redundancy for a nonparametric family of processes. The present paper gives a precis ..."
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Cited by 8 (5 self)
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Csisz ar and Shields have recently proved that the minimax redundancy for a class of (stationary) renewal processes is ( n) where n is the block length. This interesting result provides a first nontrivial bound on redundancy for a nonparametric family of processes. The present paper gives a precise estimate of the redundancy rate for such (nonstationary) renewal sources, namely, 2 n +O(log n): This asymptotic expansion is derived by complexanalytic methods that include generating function representations, Mellin transforms, singularity analysis and saddle point estimates. This work places itself within the framework of analytic information theory.
Minimax Trees in Linear Time
, 812
"... Abstract. A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves ’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffmanlike, O(nlog n)time algorithm for building ..."
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Abstract. A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves ’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffmanlike, O(nlog n)time algorithm for building them. Drmota and Szpankowski (2002) gave another O(nlog n)time algorithm, which checks the Kraft Inequality in each step of a binary search. In this paper we show how Drmota and Szpankowski’s algorithm can be made to run in linear time on a word RAM with Ω(log n)bit words. We also discuss how our solution applies to problems in data compression, group testing and circuit design. 1