Browsing by Subject "Probability distribution"
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Item Open Access An inequality on guessing and its application to sequential decoding(IEEE, 1995) Arıkan, ErdalLet (X,Y) be a pair of discrete random variables with X taking values from a finite set. 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. The main result is a tight lower bound on nonnegative moments of G(X|Y). As an application, lower bounds are given on the moments of computation in sequential decoding. In particular, a simple derivation of the cutoff rate bound for a single-user channels is obtained, and the previously unknown cutoff rate region of multi-access channels is determined.Item 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.