作者：
Sato, NKoga, HUniv Tsukuba
Masters Program Sci & Engn Tsukuba Ibaraki 3058573 Japan Univ Tsukuba
Grad Sch Syst & Informat Engn Tsukuba Ibaraki 3058573 Japan
optimistic coding is a coding in which we require the existence of reliable codes for infinitely many block length. In this letter we consider the optimistic source coding theorems for a general source Z from the info...
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optimistic coding is a coding in which we require the existence of reliable codes for infinitely many block length. In this letter we consider the optimistic source coding theorems for a general source Z from the information-spectrum approach. We first formulate the problem to be considered clearly. We obtain the optimistic infimum achievable source coding rate T-epsilon(Z) for the case where decoding error probability epsilon(n) is asymptotically less than or equal to an arbitrarily given epsilonis an element of [0, 1). In fact, T-epsilon(Z) turns out to be expressed in a form similar to the ordinary infimum achievable source coding rate. A new expression for T-epsilon(Z) is also given. In addition. we investigate the case where epsilon(n) = 0 for infinitely many n and obtain the infimum achievable coding rate.
This paper is concerned with coding theorems in the optimistic sense for separate coding of two correlated general sources X-1 and X-2. We investigate the achievable rate region R-opt(X-1, X-2) such that the decoding ...
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This paper is concerned with coding theorems in the optimistic sense for separate coding of two correlated general sources X-1 and X-2. We investigate the achievable rate region R-opt(X-1, X-2) such that the decoding error probability caused by two encoders and one decoder can be arbitrarily small infinitely often under a certain rate constraint. We give an inner and an outer bounds of R-opt(X-1, X-2), where the outer bound is described by using new information-theoretic quantities. We also give two simple sufficient conditions under which the inner bound coincides with the outer bound.
In information-spectrum methods proposed by Han and Verdu, quantities defined by using the limit superior (or inferior) in probability play crucial roles in many problems in information theory. In this paper, we intro...
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In information-spectrum methods proposed by Han and Verdu, quantities defined by using the limit superior (or inferior) in probability play crucial roles in many problems in information theory. In this paper, we introduce two nonconventional quantities defined in probabilistic ways. After clarifying basic properties of these quantities, we show that the two quantities have operational meaning in the epsilon-coding problem of a general source in the ordinary and optimistic senses. The two quantities can be used not only for obtaining variations of the strong converse theorem but also establishing upper and lower bounds on the width of the entropy-spectrum. We also show that the two quantities are expressed in terms of the smooth Renyi entropy of order zero.
Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of 2(mRL) reconstruction sequences and the secrecy is measured by the minimum distortion o...
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Recently, a secrecy measure based on list-reconstruction has been proposed, in which a wiretapper is allowed to produce a list of 2(mRL) reconstruction sequences and the secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to the one with secrecy measured by a new quantity lossy equivocation, which is proved to be the minimum optimistic one-achievable source coding rate (the minimum coding rate needed to reconstruct the source within target distortion with positive probability for infinitely many blocklengths) of the source with the wiretapped signal as two-sided information, and also can be seen as a lossy extension of conventional equivocation. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using uncoded scheme and (operationally) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the case of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proved to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product, optimistic lossy source coding has also been addressed.
Recently, a secrecy measure based on list-reconstruction has been proposed [1], in which a wiretapper is allowed to produce a list of 2 (m R L) reconstruction sequences and secrecy is measured by the minimum distortio...
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ISBN:
(纸本)9781509045501
Recently, a secrecy measure based on list-reconstruction has been proposed [1], in which a wiretapper is allowed to produce a list of 2 (m R L) reconstruction sequences and secrecy is measured by the minimum distortion over the entire list. In this paper, we show that this list secrecy problem is equivalent to one with secrecy measured by a new quantity lossy-equivocation, which is proven to be the minimum optimistic 1-achievable source coding rate of the source with the wirtapped signal as two-sided information, and also can be seen as an extension of conventional equivocation to lossy case. Upon this (or list) secrecy measure, we study source-channel secrecy problem in the discrete memoryless Shannon cipher system with noisy wiretap channel. Two inner bounds and an outer bound on the achievable region of secret key rate, list rate, wiretapper distortion, and distortion of legitimate user are given. The inner bounds are derived by using an uncoded scheme and a (operationly) separate scheme, respectively. Thanks to the equivalence between lossy-equivocation secrecy and list secrecy, the information spectrum method is leveraged to prove the outer bound. As special cases, the admissible region for the cases of degraded wiretap channel or lossless communication for legitimate user has been characterized completely. For both these two cases, separate scheme is proven to be optimal. Interestingly, however, separation indeed suffers performance loss for other certain cases. Besides, we also extend our results to characterize the achievable region for Gaussian communication case. As a side product optimistic lossy source coding has also been addressed.
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