Exponent Of Probability Research Articles

Feedback does not affect the reliability function of a DMC at rates above capacity (Corresp.)

Asymptotically coincident upper and lower bounds on the exponent of the largest possible probability of correct decoding for block codes of any given rate above capacity have been given by Dueck and Korner. Their method is extended to show that the same bounds also hold in the presence of noiseless feedback.

Reliability function of a discrete memoryless channel at rates above capacity (Corresp.)

Asymptotically coincident upper and lower bounds on the exponent of the largest possible probability of the correct decoding of block codes are given for all rates above capacity. The lower bound sharpens Omura's bound. The upper bound is proved by a new and simple combinatorial argument.

Monte Carlo experiment for the two-dimensional site percolation network

A Monte Carlo computer experiment gives the bulk conductivity of a 200*200 site square resistor network consisting of two kinds of unit resistor with difference conductance. An enumeration of clusters of one phase in the networks with 200*200 sites and 500*500 sites provides the percolation probability and an estimate of the critical probability 0.59<Pc<<0.60 for the square site system. The critical conductivity exponent is reported to be t=1.26+or-0.03 for the critical percolation probability pc=0.591+or-0.001. The critical exponent of the percolation probability is found to be s=0.20+or-0.03 for the square site system.

Use of orthogonal signaling in sequential decision feedback

Viterbi [Information and Control, 8, 80–92 (1965)] has previously considered the effect of sequential decision feedback on communication over an additive white gaussian noise channel. In particular, he analyzed a suboptimum transmission scheme using M orthogonal signals and obtained an upper bound on the error probability. In the following presentation we propose a different suboptimum system for the same problem and obtain an exact expression for the error probability. The error probability for our suboptimum scheme is always less than that for Viterbi's scheme and in fact shows significant improvement for rates near channel capacity. Figure 1 shows the improvement in terms of the channel reliability function (which is proportional to the negative exponent of the error probability).2