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On the capacity region of the multiple access half‐duplex relay channel

In this paper, we consider the transmission over multiple access relay channel (MARC) in which the relay operates in half‐duplex mode. The main contribution of this paper is establishing the capacity of the multiple access half‐duplex relay channel (MAHRC). Toward achieving this goal, we first derive a new achievable rate region. While deriving the achievable rate region, well‐known encoding and decoding schemes, which are used for transmission and reception over the degraded broadcast channel and the multiple access channel, are used. In this transmission scheme, the transmission from the two sources via the half‐duplex relay, to the destination, is split into two phases. Afterwards, an outer bound to the transmission over the discrete memoryless MAHRC is developed. Consequently, we show that the achievable rate region matches the outer bound and therefore the capacity region is formed. Further, the capacity region is extended to the case of Gaussian channel. Additionally, many numerical examples are shown to validate our theoretical derivations. In particular, these numerical examples show that the achievable rate region, and then the capacity, that we derive is larger than the well‐known results in the literature.