Duality Between the Improved Rate Regions of Gaussian Multiple Access and Broadcast Channel for Discrete Constellations
In this paper, we first look at the achievable rate regions of the Gaussian Multiple Access Channel (G-MAC) and Gaussian Broadcast Channel (G-BC) when discrete constellations are transmitted. Focusing on the two-user case and assuming uncoded Pulse Amplitude Modulation (PAM), we show that the rate regions of G-MAC and G-BC can be improved by power conservation at the transmitter, a factor ignored in the earlier derived rate regions. We then further investigate duality between the G-MAC and the G-BC and show that a rate pair achieved in the G-MAC can be translated to a rate pair in the dual G-BC, such that the equal sum power constraint be satisfied. Due to the similarity of the rate expressions to Shannons capacity formula, for an appropriate choice of signal to noise ratio (SNR) gap, we show that when finite constellations are used for transmission, rate regions of these two channels also have a dual relationship (the known for Gaussian alphabets). The rate region of the G-BC can therefore be characterized from the rate region of the dual G-MAC and vice versa.
duality gaussian multiple access channel (g-mac) gaussian broadcast channel (g-bc) pulse amplitude modulation (pam) power conservation finite constellations successive interference cancellation (sic)