Abstract- First, the Han-Kobayashi (HK) rate region for general interference channel (IC) is partially improved allowing the input random variables to be correlated. Second, considering a general input distribution and using a combination of the HK jointly decoding strategy, Marton like coding and binning scheme, we obtain a new achievable rate region for the cognitive radio channel (CRC) and show that this new region (i) is a generalized and improved version of the Devroye-Mitran-Tarokh (DMT) region, (ii) has an interesting interpretation, i.e., any rate in the region has generally three additional terms in comparison with the HK region and (iii) contains some of simply described rate regions as its subsets. Key words: Interference channel, cognitive radio channel, new

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