An achievable rate region for the 2-receiver broadcast channel obtained by viewing it as an interference channel

We derive an achievable region for the 2-receiver broadcast channel with private messages only by incorporating ideas of message splitting as in the Han-Kobayashi scheme for the interference channel. The achievable region we obtain is equivalent to the best-known achievable region under this scenario, obtained by Marton. The scheme presented here is motivated by the following question: Why does a common random variable W help improve Marton's achievable rate region when only private messages are required? Motivated by this question, we produce a region without an explicit commonly generated random variable W; instead we think of each private message being split naturally into two parts: one part that is also decoded by the other receiver, and another that is only decoded by its intended receiver.