On Identification

Abstract

In Shannon’s classical model of transmitting a message over a noisy channel we have the following situation:

There are two persons called sender and receiver. Sender and receiver can communicate via a channel. In the simplest case the sender just puts some input letters into the channel and the receiver gets some output letters. Usually the channel is noisy, i.e. the channel output is a random variable whose distribution is governed by the input letters. This model can be extended in several ways: Channels with passive feedback for example give the output letters back to the sender. Multiuser channels like multiple access channels or broadcast channels (which will not be considered in this paper) have several senders or receivers which want to communicate simultaneously. Common to all these models of transmission is the task that sender and receiver have to perform: Both have a common message setM and the sender is given a messagei∈M. He has to encode the message (i.e. transform it into a sequence of input letters for the channel) in such a way, that the receiver can decode the sequence of output letters so that he can decide with a small probability of error what the message i was. The procedures for encoding and decoding are called a code for the channel and the number of times the channel is used to transmit one message is called the blocklength of the code.