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McMaster University

1. Xu, Rui. Capacity Analysis of Finite State Channels.

Degree: PhD, 2017, McMaster University

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.


Doctor of Philosophy (PhD)

It is well known that with the knowledge of channel state, it is possible to increase the channel capacity. In this sense, knowing channel state never hurts. However, whether it is always bene cial to actively acquire channel state is another story. If we take into account the cost of measuring the channel state against the potential gain on the capacity, sometimes it may not appear very economic to do so. This thesis studies the effect of the quality of observed channel states on the channel capacity. It has been found out in some circumstances the channel capacity is very sensitive to the noise on the state information. On the other hand, it appears that the maximum capacity can be achieved with the knowledge of a small portion of the total channel state information under a slightly different setting. This thesis proves the generality of such phenomena in binary-input channels and provides the necessary and sufficient conditions for the occurrence of such phenomena for an arbitrary channel. This paper also introduces the idea of intrinsic capacity which can be used to measure the ultimate capacity potential of a channel by exploring the…

Advisors/Committee Members: Chen, Jun, Electrical and Computer Engineering.

Subjects/Keywords: channel capacity; channel state

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APA (6th Edition):

Xu, R. (2017). Capacity Analysis of Finite State Channels. (Doctoral Dissertation). McMaster University. Retrieved from

Chicago Manual of Style (16th Edition):

Xu, Rui. “Capacity Analysis of Finite State Channels.” 2017. Doctoral Dissertation, McMaster University. Accessed July 23, 2018.

MLA Handbook (7th Edition):

Xu, Rui. “Capacity Analysis of Finite State Channels.” 2017. Web. 23 Jul 2018.


Xu R. Capacity Analysis of Finite State Channels. [Internet] [Doctoral dissertation]. McMaster University; 2017. [cited 2018 Jul 23]. Available from:

Council of Science Editors:

Xu R. Capacity Analysis of Finite State Channels. [Doctoral Dissertation]. McMaster University; 2017. Available from: