### Communication channel

 Editor Díaz Nafría, J.M. jnafria@uax.es Incorporated contributions Díaz (09/01/09), Aguilar(30/9) Usage domain transdisciplinary, MTC, channel theory, situation theory Type concept French Canal de communications German Kommunikationskanal

Contents
1. In Mathematical Theory of Communication
2. In Channel theory

1. In Mathematical Theory of Communication

In the MTC and many other information and communication theories by extension, C.C. deals with the medium (or set of media) that allow(s) transmitting the signals generated by the transmitter to the receiver. As stated by Shannon: “merely the medium used to transmit the signal from transmitter to receiver. It may be a pair of wires, a coaxial cable, a band of radio frequencies, a beam of light, etc”.

It could be said that the objective of the transmission codifier is to adapt the messages, sent through the information source, to the characteristics of the channel (which has certain limitations and available resources, such as the bandwidth or frequency margin that can be sent). In the analysis, Shannon distinguishes between channels without noise (which is nothing but a theoretical abstraction that can approximately correspond to a situation in which the noise is negligible with respect to the received signals) and channels with noise (which is the normal situation and must especially be taken into consideration when the noise is notably present with respect to the signal).
A fundamental part of Shannon’s theory is aimed at finding the limits of the →information amount that can be sent to a channel with given resources (Shannon’s fundamental →theorem).

#### 2. In Channel Theory

In channel theory a channel sets up an informative relation between two situations. The fact that a channel relates two situations, s1 and s2, is formally denoted as:

Which means that the situation s1 contains information about the situation s2, given the existence of channel c.

The regularities of higher order, discriminated and individualised by an agent for a given situation, constitute a type: the information flow is caused by the existence of a type T supported by situation s1 (s1 ╞ T) transmitting information about another type T’ supported by situation s2 (s2 ╞ T’). In this schema, situations s1 and s2 are respectively named signal situation and target situation with respect to c.

In formal terms, a channel c supports a constraint between types T and T’, supported by both signal and target situations:

c ╞ TàT’

if and only if for all situations s1 and s2, when s1 ╞ T and TàT’  then s2 ╞ T’.

In other words, if the situation s1 supports type T, and there is a channel c between s1 and s2 supporting the constraint between two types of the respective situations (c╞ TàT’), then situation s2 supports type T’.

References
• BARWAISE, J. (1993) “Contraints, Channels and the Flow of Information”. Situation Theory and its Applications, 3, CSLI Lecture Notes Number 37. Standford, USA: CSLI Publicacitons,.
• DEVLIN, K. (2001). Introduction to Channel Theory, Helsinki, Finland: ESSLLI.
• SHANNON, C. E. (1948). “A Mathematical Theory of Communication”. The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October.
• SHANNON, C. y WEAVER, W. (1949), The mathematical theory of communication. Urbana: The University of Illinois Press.
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Incorporated entries

Carlos Aguilar (09/01/2009)

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J.M. Díaz (09/01/2009)

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