Window and backwards decoding achieve the same sum rate for the fading cooperative Gaussian multiple access channel

Abstract

For a two user fading Gaussian multiple access channel with user cooperation, we show that window decoding achieves the same sum rate as backwards decoding, when the encoding is done using block Markov superposition coding. We prove this result by showing that when optimum power control is employed, the additional constraints on the sum rate imposed by the use of window decoding instead of backwards decoding are never active. While doing so, we also provide some properties of power allocation that is jointly optimal with block Markov coding and window decoding.