Information Theory and Coding > Channel Capacity > What is discrete memoryless channel (DMC)?

 A discrete memoryless channel (DMC) is a statistical model with an input X = {x₀, x₁, …, x_q-1}  and an output Y = {y₀, y₁, …, y_Q-1}. During each unit of time the channel accepts an input symbol from X, and in response it generates an output symbol from Y. The channel is said to be discrete when alphabets of X and Y are both finite. Also it is said to be memoryless when the current output depends on only the current input and not on any of the previous inputs.

 

A discrete channel with probability p(Y|X) is a single-input single-output system with input random variable X taking values in X and output random variable Y taking values in Y . This probability is called channel transition probability. This probabilities P(Y/X) are determined by the channel characteristics, particularly the noise in the channel are within the control of the discrete channel encoder.

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