Information-theoretic analysis of the communication systems performances is of practical and theoretical importance. In this paper, (i) Specifically, we generalize the Cover-Chiang work on point to point channel with two-sided state information to two-receiver less noisy broadcast channel (2R-LN-BC) with different side information non-causally known at the encoder as well as the decoders, and obtain the capacity region including the previous works as its special cases. Then, (ii) the obtained result is expanded to the continuous alphabet Gaussian version. In this Gaussian version, the side information available at the receivers are supposed to be correlated on the channel noises and the impact of these receivers cognition of the noises on the capacity region is analyzed.

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