Abstract- The computation of capacity for discrete memoryless channels can be efficiently solved using the Arimoto-Blahut (AB) iterative algorithm. However, the extension of this algorithm to compute the capacity for channels with causal side information (SI) at the transmitter is not straightforward, because generally it is hard to evaluate the rates and capacities having auxiliary random variables. In this paper, we use an alternative reformulation of differential evolution optimization method to compute the capacity for channels with causal side information and introduce efficient algorithm to compute the capacity of these channels. Also we extend this algorithm to compute the sum capacity of discrete multiple access channels with causal side information at the transmitter. Keywords— Arimoto-Blahut algorithm, differential evolution algorithm, causal and non causal side

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