Constellation Shaping for Broadcast Channels in Practical Situations

This paper deals with constellation shaping for degraded broadcast channels using a finite dimension constellation, in which a single source communicates simultaneously to two receivers, with a specific interest for the situation in which each user can distinguish only between two symbols. This corresponds to a very practical situation, and hierarchical modulation is a special case of this framework. We investigate if higher achievable rates can be obtained by using non uniform constellations following a nonequiprobable distribution. Achievable rates regions are derived for Additive White Gaussian Noise (AWGN) and for finite input PAM constellations. A noticeable shaping gain (compared with the equiprobable case) is observed with 4 PAM symbols, when achievable rates are maximized over the probability distribution of the input signals, the shape of the constellation, and the labeling. 1. INTRODUCTION Current communication systems usually make use of orthogonal schemes (either in time and/or frequency) in order to address several receivers. However, it is well known since Cover [1] that if a sender wants to send information simultaneously to several receivers, given specific broadcast channel conditions, superimposing high-rate information and lowrate information may achieve higher bandwidth efficiency than the time-sharing strategy. Superposition coding has been shown to reach the theoretical capacity limit for twousers AWGN broadcast channel using an infinite Gaussian input alphabet [1].