Outage Capacity and Optimal Transmission for Dying Channels

TL;DR

This paper analyzes the outage capacity of dying channels in wireless networks, proposing optimal coding and power allocation strategies, and extends the analysis to multi-channel scenarios with different attack models.

Contribution

It introduces a new outage capacity measure for dying channels, derives optimal coding length and power allocation, and extends results to multi-channel cases with asymptotic outage probability analysis.

Findings

Optimal coding length minimizes outage probability under uniform power allocation.

Power allocation optimization can be formulated as a convex problem.

Overall outage probability approaches zero as the number of sub-channels increases under certain conditions.

Abstract

In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a \emph{dying channel}, we model it as a block-fading (BF) channel with a finite and random delay constraint. First, we define the outage capacity as the performance measure, followed by studying the optimal coding length $K$ such that the outage probability is minimized when uniform power allocation is assumed. For a given rate target and a coding length $K$, we then minimize the outage probability over the power allocation vector $\mv{P}_{K}$, and show that this optimization problem can be cast into a convex optimization problem under some conditions. The optimal solutions for several special cases are discussed. Furthermore, we extend the single point-to-point dying channel result to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the $m$-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the \emph{rate per unit cost} is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels.