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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第4期46卷 1217-1226页

作者： Han, TS Univ Electrocommun Grad Sch Informat Syst Chofu Tokyo 1828585 Japan

Given a general source X = {X-n}(n=1)(infinity), source coding is characterized by a pair (phi(n), psi(n)) of encoder phi(n) and decoder psi(n) together with the probability of error epsilon(n) = Pr{psi(n)(phi(n)(X-n)) not equal X-n}. If the length of the encoder output phi(n)(X-n) is fixed, then it is called fixed-length source coding, while if the length of the encoder output phi(n)(X-n) is variable, then it is called variable-length source coding. Usually, in the context of fixed-length source coding the probability of error epsilon(n) is required to asymptotically vanish (i.e., lim(n-->infinity) epsilon(n) = 0), whereas in the context of variable-length source coding the probability of error epsilon(n) is required to be exactly zero (i.e., epsilon(n) = 0 For All n = 1, 2,....) In contrast to these, we consider in the present paper the problem of variable-length source coding with asymptotically vanishing probability of error (i.e., lim(n-->infinity) epsilon(n) = 0), and establish several fundamental theorems on this new subject.

关键词： countably infinite source alphabet fixed-length source coding general source uniform integrability variable-length source coding weak sup-entropy rate weak variable-length source coding

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Optimum Overflow Thresholds in variable-length source coding Allowing Non-Vanishing Error Probability

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第12期65卷 8213-8221页

作者： Nomura, Ryo Yagi, Hideki Waseda Univ Ctr Data Sci Tokyo 1620042 Japan Univ Electrocommun Dept Comp & Network Engn Koganei Tokyo 1848795 Japan

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources.

关键词： Error probability general source overflow probability variable-length source coding

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The optimal overflow and underflow probabilities of variable-length coding for the general source

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年第10期E84A卷 2457-2465页

作者： Uchida, O Han, TS Kanagawa Inst Technol Dept Network Engn Atsugi Kanagawa 2430292 Japan Univ Electrocommun Grad Sch Informat Syst Chofu Tokyo 1828585 Japan

In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent r always coincides with the infimum achievable fixed-length coding rate given the error exponent r, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.

关键词： overflow probability underflow probability general source variable-length source coding reliability function

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GENERATING RANDOM BITS FROM AN ARBITRARY source - FUNDAMENTAL LIMITS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1995年第5期41卷 1322-1332页

作者： VEMBU, S VERDU, S PRINCETON UNIV DEPT ELECT ENGN PRINCETON NJ 08544 USA

Suppose we are given a random source and want to use it as a random number generator;at what rate can we generate fair bits from it? We address this question in an information-theoretic setting by allowing for some arbitrarily small but nonzero deviation from ''ideal'' random bits. We prove our results with three different measures of approximation between the ideal and the obtained probability distributions: the variational distance, the d-bar distance, and the normalized divergence. Two different contexts are studied: fixed-length and variable-length random number generation. The fixed-length results of this paper provide an operational characterization of the inf-entropy rate of a source, defined in Han and Verdu [1] and the variable-length results characterize the liminf of the entropy rate, thereby establishing a pleasing duality with the fundamental limits of source coding. A feature of our results is that we do not restrict ourselves to ergodic or to stationary sources.

关键词： SHANNON THEORY RANDOM NUMBER GENERATION ENTROPY FIXED-length source coding variable-length source coding APPROXIMATION THEORY

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ZERO-REDUNDANCY coding FOR UNEQUAL CODE SYMBOL COSTS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1992年第5期38卷 1583-1586页

作者： ABRAHAMS, J LIPMAN, MJ Mathematical Sciences Division Office of Naval Research Arlington VA USA

source distributions that can be encoded with zero redundancy for the case of unequal code symbol costs are examined. These distributions provide a natural generalization of the binary, equal costs case for which these distributions are the dyadic distributions. These zero redundancy codes have the property that the expected proportion of codeword symbols given by a particular letter is equal to an exponential function of the code letter cost. The converse is not true in general, however partial converse results hold. Maximum-entropy zero-redundancy distributions are easily identified through their connection with unequal cost coding for uniform sources.

关键词： variable-length source coding ZERO REDUNDANCY UNEQUAL COSTS

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