The road to achieve the capacity of the three-way degraded broadcast channel

Abstract

In this paper, we consider the discrete memory-less three-way degraded broadcast channel (3WDBC). The main contribution of this paper is in characterizing the capacity region of the discrete memoryless 3WDBC. To end up with this goal, we first develop the achievable region. Then, an outer bound to the capacity region is also derived. Next, the achievable region is shown to meet the outer bound such that the capacity is achieved. After that, the 3WDBC is shown to encompass many well-known multi-user networks such as (i) broadcast channel, (ii) multiple access channel, (iii) two-way channel, and (iv) relay channel. Further, the achievable capacity region is then extended to the additive Gaussian noise channel. Specifically, superposition encoding is employed at each user such that a given user can appropriately allocate its power to broadcast to the other two users. In this direction, two design criteria are theoretically presented and numerically investigated to show the range that the power allocation factor at each user may have.