Probabilistic packet transmission through a limited-lifetime deletion channel with arbitrary deletion probability

Abstract

This paper considers the transmission of a packet through a binary deletion channel with an unknown and arbitrarily high deletion probability. The deletion positions are unknown to both sender and receiver, and the number of bits received before channel closure is unknown to both sender and receiver. The number of received bits is in the range 1-100. This paper argues that, for such a channel, an encoding method that enables the calculation of probability masses for all possible packets is preferred to one which attempts perfect reconstruction of the transmitted packet. It then presents and analyzes such an encoding method. The presented method encodes information on the probability of receiving a 1 vs. a 0, rather than in the 1's and 0's themselves. The receiver decodes the information using Bayesian inference. Rather than transmitting the packet of interest, the encoding method transmits information about the packet of interest in order to guarantee information transfer for any nonzero number of bits received. This paper analyzes the statistics of convergence of this estimator for all numbers of received bits from 0 to 100.