Electrical Engineering-Systems Dept.

*** SEMINAR ***

Yuval Lomnitz

(Ph.D. student under the supervision of Prof. Meir Feder, TAU)

on the subject:

Universal communication over unknown channels

Traditional information theory and communication theory assume the channel between the transmitter and the receiver is characterized by a known probabilistic behavior. In this talk we take the other extreme, and consider the problem of communication over an unknown channel, while attempting to minimize any assumptions on the channel.

A slow feedback link is assumed, by which the transmitted signal can be adapted to the empirical channel. Two main settings are considered. In the first setting, no probabilistic model for the channel is assumed, and the communication rate is determined as a function of the input and output sequences known a-posteriori (a rate-function). As an example, the empirical mutual information between the input and output vectors, is achievable, without making any assumption on the channel.

In the second setting, there exists a vector-wise probabilistic model for the channel, characterizing the probability of any output sequence, given any input sequence, but this model is unknown. The target is to find a universal system that, without knowing the channel, communicates as well as any reference communication system, from a given reference class.

In the particular case where the channel is memoryless in the input, then by universal adaptation of the codebook distribution (prior), the capacity of the time-averaged channel can be attained. The more interesting result is that for a general channel with memory and possibly arbitrary time variation, there is a universal system with feedback that, without channel knowledge, and under mild assumptions on the channel, asymptotically performs at least as well as any finite block code designed knowing the channel.