Abstract
Recently, due to the fundamental nature, the coding problem of interference channels in multi-user information theory, is vigorously tackled by many communication theorists. Especially, in order to understand the essential character, the situation with two couples of sender and receiver has been well studied. Among a lot of results, the achievable region, so-called the HK region, given by Han and Kobayashi in 1981 continues to be the best single-letter expression for the general interference channel up to today. In this survey paper, we elucidate the details of the HK region, the study to simplify the expression of HK region, and give the explanation on subclasses of interference channels for which the capacity problem has been already fixed. Further, we explain the result by Etkin, Tse, Wang. They showed the asymptotic optimality for Gaussian interference channels by using a simple case of the HK scheme when SNR and INR tend to very large. Moreover, quite recently, by demonstrating the existence of an achievable rate pair outside the HK region, Nair, et.al., show that the optimality of HK region now breaks. Thus, we are now faced with a historical turning point in the study on the interference channel.
