منابع مشابه
Minimax Rényi redundancy
The redundancy for universal lossless compression in Campbell’s setting is characterized as a minimax Rényi divergence, which is shown to be equal to the maximal α-mutual information via a generalized redundancy-capacity theorem. Special attention is placed on the analysis of the asymptotics of minimax Rényi divergence, which is determined up to a term vanishing in blocklength.
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If optimality is measured by average codeword length, Huffman's algorithm gives optimal codes, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the d...
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Let Xn = (X1; ; Xn) be a memoryless source with unknown distribution on a finite alphabet of size k. We identify the asymptotic minimax coding redundancy for this class of sources, and provide a sequence of asymptotically minimax codes. Equivalently, we determine the limiting behavior of the minimax relative entropy minQ maxP D(PX kQX ), where the maximum is over all independent and identically...
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Consider the problem of finite-rate filtering of a discrete memoryless process {Xi}i≥1 based on its noisy observation sequence {Zi}i≥1, which is the output of a Discrete Memoryless Channel (DMC) whose input is {Xi}i≥1. When the distribution of the pairs (Xi, Zi), PX,Z , is known, and for a given distortion measure, the solution to this problem is well known to be given by classical rate-distort...
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We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers. We show that the mean squared distortion of a vector quantizer designed from n i.i.d. data points using any design algorithm is at least n 1=2 away from the optimal distortion for some distribution on a bounded subset of Rd. Together with existing upper bounds this result s...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2018
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2018.2803070