Browsing by Subject "Estimation theory"

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Open Access
An inequality on guessing and its application to sequential decoding
(Institute of Electrical and Electronics Engineers, 1996-01) Arikan, E.
Let (X,Y) be a pair of discrete random variables with X taking one of M possible values, Suppose the value of X is to be determined, given the value of Y, by asking questions of the form "Is X equal to x?" until the answer is "Yes". Let G(x|y) denote the number of guesses in any such guessing scheme when X=x, Y=y. We prove that E[G(X|Y)/sup /spl rho//]/spl ges/(1+lnM)/sup -/spl rho///spl Sigma//sub y/[/spl Sigma//sub x/P/sub X,Y/(x,y)/sup 1/1+/spl rho//]/sup 1+/spl rho// for any /spl rho//spl ges/0. This provides an operational characterization of Renyi's entropy. Next we apply this inequality to the estimation of the computational complexity of sequential decoding. For this, we regard X as the input, Y as the output of a communication channel. Given Y, the sequential decoding algorithm works essentially by guessing X, one value at a time, until the guess is correct. Thus the computational complexity of sequential decoding, which is a random variable, is given by a guessing function G(X|Y) that is defined by the order in which nodes in the tree code are hypothesized by the decoder. This observation, combined with the above lower bound on moments of G(X|Y), yields lower bounds on moments of computation in sequential decoding. The present approach enables the determination of the (previously known) cutoff rate of sequential decoding in a simple manner; it also yields the (previously unknown) cutoff rate region of sequential decoding for multiaccess channels. These results hold for memoryless channels with finite input alphabets.
Open Access
Theoretical limits for estimation of periodic movements in pulse-based UWB systems
(Institute of Electrical and Electronics Engineers, 2007) Gezici, Sinan
In this paper, Cramer-Rao lower bounds (CRLBs) for estimation of signal parameters related to periodically moving objects in pulse-based ultra-wideband (UWB) systems are presented. The results also apply to estimation of vital parameters, such as respiration rate, using UWB signals. In addition to obtaining the CRLBs, suboptimal estimation algorithms are also presented. First, a single-path channel with additive white Gaussian noise is considered, and closed-form CRLB expressions are obtained for sinusoidal object movements. Also, a two-step suboptimal algorithm is proposed, which is based on time delay estimation via matched filtering followed by least-squares estimation, and its asymptotic optimality property is shown in the limit of certain system parameters. Then, a multipath environment is considered, and exact and approximate CRLB expressions are derived. Moreover, suboptimal schemes for parameter estimation are studied. Simulation studies are performed for the estimation of respiration rates in order to evaluate the lower bounds and performance of the suboptimal algorithms for realistic system parameters.