Adeel Mahmood

Adeel Mahmood, Aaron B. Wagner

Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power $Γ$ as well as on finer statistics of the input power. We introduce a multifaceted power model in which the expectation of an arbitrary (but finite) number of arbitrary functions of the normalized average power is constrained. The framework generalizes existing models, recovering the standard maximal and expected power constraints and the recent mean and variance constraint as special cases. Under certain growth and continuity assumptions on the functions, our main theorem gives an exact characterization of the minimum average error probability for Gaussian channels as a function of the first- and second-order coding rates. The converse proof reduces the code design problem to minimization over a compact (under the Prokhorov metric) set of probability distributions, characterizes the extreme points of this set and invokes the Bauer's maximization principle. Our results for the multifaceted power model serve as more precise benchmarks for practical modulation schemes with multiple amplitude levels, probabilistic shaping and nonuniform constellation geometries.

Adeel Mahmood

We study a variant of unequal error protection in channel coding, where the message bit string is divided into a finite number of blocks and the maximization objective is a weighted sum of per-block decoding success probabilities. The channel model is quasi-static Rayleigh fading with channel state information available to the receiver but unavailable to the transmitter. We analyze the asymptotic and finite blocklength performance of two achievability schemes, one based on power-domain superposition (PDS) and another based on orthogonal resource allocation (ORA), also known as time-sharing. Upper bounds on the optimal number of blocks to transmit are derived. Algorithms to compute the optimal power and time splits for the two schemes are given. Simplified algorithms to compute locally optimal power and time splits are also given. Our results show that PDS outperforms ORA, but the performance differential is less than 2% in both the asymptotic and finite blocklength regimes (Figures 4 - 6). For both PDS and ORA, numerical results also upper bound the gap between the asymptotic and finite blocklength performance by approximately 10% for n = 1000 and 3% for n = 5000 (Figures 7 - 10).