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A method of coding (see [[Coding and decoding|Coding and decoding]]) in which to every possible value of a message produced by a source of information (cf. [[Information, source of|Information, source of]]) is assigned a randomly chosen value of the signal at the input of the [[Communication channel|communication channel]]. On the set of values of the signals at the input of the channel a certain probability distribution is given. It is often assumed that every element of the code (that is, the value of a signal at the input corresponding to a given value of the information) is chosen independently of the others and in accordance with a given probability distribution. Sometimes a random coding is defined in such a way that every realization of it is a group code.

The importance of random coding is related to the fact that the probability of erroneous decoding (cf. [[Erroneous decoding, probability of|Erroneous decoding, probability of]]), averaged over all realizations, gives a relatively easy to compute upper bound for the probability of erroneously decoding an optimal code.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  C.E. Shannon,   "A mathematical theory of communication"  ''Bell. System Techn. J.'' , '''27'''  (1948)  pp. 979–423; 623–656</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  R.L. Dobrushin,   "A general formulation of the fundamental theorem of Shannon in information theory"  ''Uspekhi Mat. Nauk'' , '''14''' :  6  (1959)  pp. 3–104  (In Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  R. Gallagher,   "Information theory and reliable communication" , Wiley  (1968)</TD></TR></table>