For a fixed total bandwidth expansion factor, and for a fixed channel code rate, we consider the problem of optimal bandwidth allocation between the source coder and the spread-spectrum unit for a multicarrier direct-...
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For a fixed total bandwidth expansion factor, and for a fixed channel code rate, we consider the problem of optimal bandwidth allocation between the source coder and the spread-spectrum unit for a multicarrier direct-sequence CDMA system operating over a frequency-selective fading channel with narrowband interference. Assuming a Gaussian source with the optimum scalar quantizer and a binary convolutional code with soft-decision decoding, we obtain both a lower and an upper bound on the end-to-end average source distortion. The optimal bandwidth allocation is then numerically computed by minimizing upper and lower bounds on the average distortion. We show that the upper bound based cost function is a convex function of the source code rate, and the optimal allocation depends on the system and the channel conditions, such as the total number of active users, the number of carriers, and the average jammer-to-signal power ratio.
We derive a lower bound on each supporting hyperplane of the rate region of the vector Gaussian multiterminal source coding problem by coupling it with the CEO problem through a limiting argument. The tightness of thi...
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We derive a lower bound on each supporting hyperplane of the rate region of the vector Gaussian multiterminal source coding problem by coupling it with the CEO problem through a limiting argument. The tightness of this lower bound in the high-resolution regime and the weak-dependence regime is proved.
We study the problem of the reconstruction of a Gaussian field defined in [0,1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field w...
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We study the problem of the reconstruction of a Gaussian field defined in [0,1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field with a given mean square distortion. We consider a class of two-stage mechanisms which (a) send information to allow the reconstruction of the sensor's samples within sufficient accuracy, and then (b) use these reconstructions to estimate the entire field. To implement the first stage, the heavy correlation between the sensor samples suggests the use of distributed coding schemes to reduce the total rate. Our main contribution is to demonstrate the existence of a distributed block coding scheme that achieves, for a given fidelity criterion for the sensor's measurements, a total information rate that is within a constant, independent of N, of the minimum information rate required by an encoder that has access to all the sensor measurements simultaneously. The constant in general depends on the autocorrelation function of the field and the desired distortion criterion for the sensor samples.
The redundancy of a source code is the difference between its expected performance and the optimum performance theoretically attainable (OPTA). In an analysis of the redundancy problem of source coding the aim is to i...
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The redundancy of a source code is the difference between its expected performance and the optimum performance theoretically attainable (OPTA). In an analysis of the redundancy problem of source coding the aim is to investigate the trade-off between the minimum redundancy over a class of codes having a common parameter (such as block length) and the common parameter. We assume that the common parameter associated with the codes considered is block length. We refer to the minimum redundancy over the class of all codes having block length n and some specified type as the nth-order redundancy. In lossless source coding, the OPTA is the Shannon entropy and there exists extensive literature studying the nth-order redundancy. Before our work, nontrivial lower bounds are still unknown to either the n-th order rate redundancy or the n-th order distortion redundancy. The aim of this paper is to answer the question of whether Pilc's (1968) lower bound is true. We derive a closed formula for the nth-order distortion redundancy and prove the formula for the upper and lower bounds of the nth-order rate redundancy.
We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff betwe...
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We study secure source-coding with causal disclosure, under the Gaussian distribution. The optimality of Gaussian auxiliary random variables is shown in various scenarios. We explicitly characterize the tradeoff between the rates of communication and secret key. This tradeoff is the result of a mutual information optimization under Markov constraints. As a corollary, we deduce a general formula for Wyner's Common Information in the Gaussian setting.
We consider the cascade rate-distortion problem where side information is known to the source encoder and to the first user but not to the second user. We characterize the rate-distortion region for this problem. For ...
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ISBN:
(纸本)9781424463725
We consider the cascade rate-distortion problem where side information is known to the source encoder and to the first user but not to the second user. We characterize the rate-distortion region for this problem. For the quadratic Gaussian case we show that it is enough to consider jointly Gaussian distributions; a fact that leads to an explicit solution.
A novel lossless source coding paradigm applies to problems of unreliable lossless channels with low bit rates, in which a vital message needs to be transmitted prior to termination of communications. This paradigm ca...
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ISBN:
(纸本)142440505X
A novel lossless source coding paradigm applies to problems of unreliable lossless channels with low bit rates, in which a vital message needs to be transmitted prior to termination of communications. This paradigm can be applied to Alfred Renyi's secondhand account of an ancient siege in which a spy was sent to scout the enemy but was captured. After escaping, the spy returned to his base in no condition to speak and unable to write. His commander asked him questions that he could answer by nodding or shaking his head, and the fortress was defended with this information. Renyi told this story with reference to prefix coding, but maximizing probability of survival in the siege scenario is distinct from yet related to the traditional source coding objective of minimizing expected codeword length. Rather than finding a code minimizing expected codeword length Xi n i=1 p(i)l(i), the siege problem involves maximizing Xi n i=1 p(i)thetas l(i) for a known thetas isin (0,1). When there are no restrictions on codewords, this problem can be solved using a known generalization of Huffman coding. The optimal solution has coding bounds which are functions of Renyi entropy; in addition to known bounds, new bounds are derived here. The alphabetically constrained version of this problem has applications in search trees and diagnostic testing. A novel dynamic programming algorithm - based upon the oldest known algorithm for the traditional alphabetic problem - optimizes this problem in O(n 3 ) time and O(n 2 ) space, whereas two novel approximation algorithms can find a suboptimal solution faster: one in linear time, the other in O(n log n). coding bounds for the alphabetic version of this problem are also presented
We consider secure multi-terminal source coding problems in the presence of a public helper. Two main scenarios are studied: 1) source coding with a helper where the coded side information from the helper is eavesdrop...
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ISBN:
(纸本)9781479904440
We consider secure multi-terminal source coding problems in the presence of a public helper. Two main scenarios are studied: 1) source coding with a helper where the coded side information from the helper is eavesdropped by an external eavesdropper, 2) triangular source coding with a helper where the helper is considered as a public terminal. We are interested in how the helper can support the source transmission subject to a constraint on the amount of information leaked due to its public nature. We characterize the tradeoff between transmission rate, incurred distortion, and information leakage rate at the helper/eavesdropper in the form of a rate-distortion-leakage region for various classes of problems.
The problem of source coding with side information at the decoder arises in many practical scenarios. Although this problem has been well characterized in information theory, particularly by the work of Wyner and Ziv ...
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ISBN:
(纸本)0769510310
The problem of source coding with side information at the decoder arises in many practical scenarios. Although this problem has been well characterized in information theory, particularly by the work of Wyner and Ziv (1976), there is still lack of successful algorithms for it. In this paper, we use trellis codes to approach the theoretical limit. An embedded trellis code structure is proposed, and its properties are examined. Using this structure, we can achieve the granular gain at the encoder as well as the coding gain at the decoder. Simulation results show that the proposed scheme outperforms the algorithms reported in the literature. It is also indicated that the performance of the proposed algorithm can approach the information-theoretic limit at high rate as the trellis complexity increases.
Modern mathematical proofs are becoming so big that they cause a problem of trust. Formal verification using proof-assistants has recently emerged as a solution to ensure the correctness of big proofs. Before being ab...
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Modern mathematical proofs are becoming so big that they cause a problem of trust. Formal verification using proof-assistants has recently emerged as a solution to ensure the correctness of big proofs. Before being able to verify formally big proofs one must build substantial libraries of formal definitions and formal theorems. In this paper, we explain how we contribute to an existing formalization of information theory by extending it with a foundational theorem; namely, the variable-length source coding theorem.
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