Chapman–Robbins bound

Abstract: We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett 's bound based on the Renyi entropy of order 2 because the bound obtained here uses the Renyi entropy of order 1+s for s ∈ [0,1]. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi 's exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.

Abstract: In Part I of this paper, we introduced the paradigm of network error correction as a generalization of classical link-by-link error correction. We also obtained the network generalizations of the Hamming bound and the Singleton bound in classical algebraic coding theory. In Part II, we prove the network generalization of the Gilbert-Varshamov bound and its enhancement. With the latter, we show that the tightness of the Singleton bound is preserved in the network setting. We also discuss the implication of the results in this paper. Definition 2. An etwork code ist-error-correcting if it can correct all τ -errors for τ ≤ t, i.e., if the total number of errors in the network is at most t, then the source message can be recovered by all the sink nodes u ∈U.A network code is Y-error-correcting if it can correct E-errors for all E ∈ Y. In Part I, we have proved the network generalizations of the Hamming bound and the Singleton bound. In this part, we will prove a network generalization of the Gilbert-Varshamov bound and its enhancement. With the latter, we will show that the tightness of the Singleton bound is preserved in the network setting. The rest of Part II is organized as follows. In Section 2, we prove the Gilbert bound and the Varshamov bound for network error-correcting codes. In Section 3, we sharpen the Varshamov bound obtained in Section 2 to the strengthened Varshamov bound. By means of the latter, we prove the tightness of the Singleton bound for

Abstract: This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems.

Abstract: We study single-term exponential-type bounds (also known as Chernoff-type bounds) on the Gaussian error function. This type of bound is analytically the simplest such that the performance metrics in most fading channel models can be expressed in a concise closed form. We derive the conditions for a general single-term exponential function to be an upper or lower bound on the Gaussian error function. We prove that there exists no tighter single-term exponential upper bound beyond the Chernoff bound employing a factor of one-half. Regarding the lower bound, we prove that the single-term exponential lower bound of this letter outperforms previous work. Numerical results show that the tightness of our lower bound is comparable to that of previous work employing eight exponential terms.