On the Outage Capacity of a Dying Channel

In this paper, we investigate a new type of channels named as "dying" channels, which are resulted in wireless networks subject to random fatal impacts, e.g., sensor networks under sudden physical attacks or cognitive radio networks with unpredictable primary user occupancy. Under such circumstances, it is critical to quantify how fast and reliable information can be collected over "dying" links. In this paper, we focus on a simple point-to-point communication setting and model the "dying" channel by the traditional if-block block-fading (BF) model subject to a fatal attack that may happen randomly in any of the K blocks. The resultant channel is non-ergodic and delay-limited in nature, and thus its information-theoretic limit can be measured by adopting the conventional outage capacity concept. An outage event in a "dying" channel could be caused by two mechanisms: fading over finite K blocks; and random attack within K blocks. In this paper, we present the general problem formulation to determine the outage capacity of the "dying" channel, as well as the corresponding optimal transmit power allocation over the K blocks, based upon the known probability distributions of both the fading channel and the attack time. The optimal power allocation turns out to be in general nonuniform with a decreasing profile over transmission blocks. In addition, there exists an optimal number of blocks over which the codeword is spanned. Some other interesting observations are also made pertinent to the optimal transmission over a "dying" channel.