Generalized Coding Theorem with Different Source Coding Schemes

Abstract

In the present paper we have consider a parametric generalization of mean codeword length and for this we have proved generalized source coding theorems. To transmit text written in the source alphabet in the form of code alphabetic character we have to associate a code word to represent each source alphabet word that we might wish to send, hence we have also verified generalized source coding theorem by using source coding schemes. Kraft’s theorem states the condition which the lengths of codewords must meet to be a prefix codes. It may seem restrictive to limit ourselves to prefix codes, as uniquely decipherable codes are not always prefix codes. The Shannon-Fano encoding scheme is based on the principle that each code bit, which can be described by a random variable, must have a maximum entropy, so we have also discussed different type of source coding schemes by taking some suitable examples.