Concatenated coding for packet transmission over the collision channel

We consider a collision channel (Massey and Mathys 1985) with additive white Gaussian noise (AWGN) and slow fading. We assume that data on a collided slot are completely lost. Caire et al. (1998) proposed a combination of signal-space coding and slow time-frequency hopping for this channel. Code vectors (or equivalently, signals) are points in a D-dimensional real Euclidean space. The main idea is that, under certain conditions on the signal-space code and provided that signal points are transmitted so that their D components belong to different time-frequency slots, even if k<D slots collide the signal can be correctly detected from its D-k uncollided components. We defined a class of signal-space codes called collision resistant modulation (CRM) with the above property. The six 2-dimensional projections of a 4-dimensional CRM are shown