Empirical Output Distribution of Good Delay-Limited Codes for Quasi-Static Fading Channels

TL;DR

This paper analyzes the output distribution of delay-limited codes in quasi-static fading channels, showing that capacity-achieving codes induce output distributions close to the ideal, with convergence results applicable even for non-vanishing error probabilities.

Contribution

It provides a rigorous empirical characterization of the output distribution for capacity-achieving delay-limited codes in fading channels, extending previous results to non-vanishing error regimes.

Findings

Normalized relative entropy between actual and ideal output distributions converges to zero.

Results apply to codes with vanishing and non-vanishing error probabilities.

Supports design of reliable delay-sensitive wireless communication systems.

Abstract

This paper considers delay-limited communication over quasi-static fading channels under a long-term power constraint. A sequence of length-$n$ delay-limited codes for a quasi-static fading channel is said to be capacity-achieving if the codes achieve the delay-limited capacity, which is defined to be the maximum rate achievable by delay-limited codes. The delay-limited capacity is sometimes referred to as the zero-outage capacity in wireless communications. The delay-limited capacity is the appropriate choice of performance measure for delay-sensitive applications such as voice and video over fading channels. It is shown that for any sequence of capacity-achieving delay-limited codes with vanishing error probabilities, the normalized relative entropy between the output distribution induced by the length-$n$ code and the $n$-fold product of the capacity-achieving output distribution, denoted by $\frac{1}{n}D(p_{Y^n}\|p_{Y^n}^*)$, converges to zero. Additionally, we extend our convergence result to capacity-achieving delay-limited codes with non-vanishing error probabilities.