Fading multi-access channels in the wideband regime: the impact of delay constraints

Incorporating delay constraints in Shannon theoretic settings is a perennial challenge. In fading channels, it is essential to specify: (1) the duration of a codeword with respect to the fading process coherence time, and (2) the time interval on which the average input power constraint is enforced. Although vanishing error probability is unattainable unless the number of degrees of freedom grows without bound, that number grows with the product of time duration and bandwidth. Thus, in the wideband regime, an asymptotic analysis is feasible even in a setting of fixed duration codebooks. We consider a block-fading model where a codeword spans a frame of N of slots, with fading constant over each slot and varying independently from slot to slot, and the power constraint is enforced on a per-codeword basis. Moreover, we assume that the sequence of fading coefficients affecting the transmission of a codeword is causally revealed to the transmitters and we allow variable-rate coding so that users can coordinate their rates in order to be always inside the fading-dependent capacity region.