Abstract

In his world-famous paper of 1948, Shannon defined channel capacity as
the ultimate rate at which information can be transmitted over a
communication channel with an error probability that will vanish if we
allow the blocklength to get infinitely large. While this result is of
tremendous theoretical importance, the reality of practical systems
looks quite different: no communication system will tolerate an
infinite delay caused by an extremely large blocklength. On the other
hand, it is not necessary to have an error probability that is exactly
zero either, a small, but finite value will suffice.

Therefore, the question arises what can be done in a practical
scheme. In particular, what is the maximal rate at which information
can be transmitted over a communication channel for a given fixed
maximum blocklength (i.e., a fixed maximum delay) if we allow a
certain maximal probability of error? In this project, we have started
to study these questions.

Keywords

Channel capacity, binary asymmetric channel (BAC), finite
blocklengths, good codes, probability of error.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Sat Jun 6 22:42:04 UTC+8 2009