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Optimal Prefix Codes And Huffman Codes
International Journal of Computer Mathematics, 2003Existence of the optimal prefix codes is shown in this paper. Relationship between the optimal prefix code and the Huffman code is also discussed. We prove that all Huffman codes are optimal prefix codes and conversely optimal prefix codes need not be Huffman codes.
Long, D., Jia, W., Li, M.
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Communications of the ACM, 1969
Methods of analyzing the control flow and data flow of programs during compilation are applied to transforming the program to improve object time efficiency. Dominance relationships, indicating which statements are necessarily executed before others, are used to do global common expression elimination and loop identification.
Edward S. Lowry, C. W. Medlock
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Methods of analyzing the control flow and data flow of programs during compilation are applied to transforming the program to improve object time efficiency. Dominance relationships, indicating which statements are necessarily executed before others, are used to do global common expression elimination and loop identification.
Edward S. Lowry, C. W. Medlock
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Optimal causal coding - decoding problems
IEEE Transactions on Information Theory, 1983This paper investigates the effect of delay constraints on the encoding of a Markov source. That optimal encoding with delay constraints can be formulated as a Markov decision problem to which standard dynamic programming methods can be applied. The case of a symmetric channel is of some interest. It is shown that for such a channel, real time encoding
Walrand, Jean C., Varaiya, Pravin
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IEEE Transactions on Information Theory, 1969
Some known results on the nonexistence of linear optimal codes can be very easily proved using results on the weight distribution of such codes.
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Some known results on the nonexistence of linear optimal codes can be very easily proved using results on the weight distribution of such codes.
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SIAM Journal on Algebraic Discrete Methods, 1983
It has been observed that not all the entries of $M( T )$, the distance matrix for a tree T, are necessary to determine T uniquely. For example, the submatrix of distances between end-vertices uniquely determines T. In this paper it is shown when T is canonically ordered, $2n - 3$ of the distances between the n end-vertices suffice for this ...
Chaiken, S. +2 more
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It has been observed that not all the entries of $M( T )$, the distance matrix for a tree T, are necessary to determine T uniquely. For example, the submatrix of distances between end-vertices uniquely determines T. In this paper it is shown when T is canonically ordered, $2n - 3$ of the distances between the n end-vertices suffice for this ...
Chaiken, S. +2 more
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Communications on Pure and Applied Mathematics, 1986
AbstractWe consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p(x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded.
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AbstractWe consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p(x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded.
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IEEE Transactions on Space Electronics and Telemetry, 1964
This paper provides an analysis of a continuous, coded ranging scheme. By the use of a Boolean function, several "component" sequences are encoded into a transmitted signal. The receiver correlates the delayed return signal with different Boolean combinations of delayed replicas of the components to determine separately the time delay of each component
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This paper provides an analysis of a continuous, coded ranging scheme. By the use of a Boolean function, several "component" sequences are encoded into a transmitted signal. The receiver correlates the delayed return signal with different Boolean combinations of delayed replicas of the components to determine separately the time delay of each component
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2012
As the previous chapters have shown, multiple techniques are available in R for powerful data-driven insights and analysis. For the average business analyst, well-designed GUID tools that are stable to use, pull data and models, and report them are essential, and all these are available within various R subcomponents and packages. This chapter is aimed
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As the previous chapters have shown, multiple techniques are available in R for powerful data-driven insights and analysis. For the average business analyst, well-designed GUID tools that are stable to use, pull data and models, and report them are essential, and all these are available within various R subcomponents and packages. This chapter is aimed
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Symbolic Debugging of Optimized Code
ACM Transactions on Programming Languages and Systems, 1982The long standing conflict between the optimization of code and the ability to symbolically debug the code is examined. The effects of local and global optimizations on the variables of a program are categorized and models for representing the effect of optimizations are given. These models are used by algorithms which determine the subset of variables
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Sequences of optimal identifying codes
IEEE Transactions on Information Theory, 2002Summary: Locating faulty processors in a multiprocessor system gives the motivation for identifying codes. Denote by \(l\) the maximum number of simultaneously malfunctioning processors. In this correspondence, we show that if \(l\geq3\), then the problem of finding the smallest cardinality of a \((1,\leq l)\)-identifying code in a binary hypercube is ...
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