Capacity Analysis of Finite State Channels

Abstract

Channels with state model communication settings where the channel statistics are not fully known or vary over transmissions. It is important for a communication system to obtain the channel state information in terms of increasing channel capacity. This thesis addresses the effect of the quality of state information on channel capacity. Extreme scenarios are studied to reveal the limit in increasing channel capacity with the knowledge of state information.

We consider the channel with the perfect state information at the decoder, while the encoder is only available to a noisy state observation. The effect of the noisy state at the encoder to the channel capacity is studied. We show that for any binary-input channel if the mutual information between the noisy state observation at the encoder and the true channel state is below a positive threshold determined solely by the state distribution, then the capacity is the same as that with no encoder side information. A complementary phenomenon is also revealed for the generalized probing capacity. Extensions beyond binary-input channels are developed.

We further investigate the channel capacity, when the causal channel state information (available at the encoder or the decoder or both) makes it deterministic. Every such a capacity is called an intrinsic capacity of the channel. Among them, the smallest and the largest called the lower and the upper intrinsic capacities, are particularly studied. Their exact values are determined in most cases when the input or the output is binary. General lower and upper bounds are also provided for the lower and the upper intrinsic capacities with causal state information available at both sides. Byproducts of this work are a generalization of the Birkhoff-von Neumann theorem and a result on the uselessness of causal state information at the encoder.