In the model of a digital communication system described in Section 1.1,we recall that the transmitter building blocks consist of the discrete-input ,discrete-output channel encoder followed by the modulator .The function of the discrete channel encord is to introduce,in a controlled manner,some redundancy in the binary information sequence ,which can be used at the receiver to overcome the effects of noise and interference encountered in the transmission of the signal through the channel. The encoding process generally involves taking k information bits at a time and mapping each k-bit sequence into a unique n-bit sequence,called a code word.The amount of redundancy introduced by the encoding of the date in this manner is measured by the ratio n/k. The reciprocal of the ratio,namely k/n,is called the code rate.