# 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.

## Keywords

Conditional Entropy Stochastic Matrix Feedback Channel Multiple Access Channel Input Alphabet## Preview

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