On Capacity of the Dirty Paper Channel with Fading Dirt in the Strong Fading Regime

The classical writing on dirty paper capacity result establishes that full interference pre-cancellation can be attained in Gelfand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the idealized assumption that perfect channel knowledge is available at both transmitter and receiver. While channel knowledge at the receiver can be obtained through pilot tones, transmitter channel knowledge is harder to acquire. For this reason, we are interested in characterizing the capacity under the more realistic assumption that only partial channel knowledge is available at the transmitter. We study, more specifically, the dirty paper channel in which the interference sequence in multiplied by fading value unknown to the transmitter but known at the receiver. For this model, we establish an approximate characterization of capacity for the case in which fading values vary greatly in between channel realizations. In this regime, which we term the strong fading regime, the capacity pre-log factor is equal to the inverse of the number of possible fading realizations

On the Dirty Paper Channel with Fast Fading Dirt

Costa`s "writing on dirty paper" result establishes that full state pre-cancellation can be attained in the Gel`fand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumptions that full channel knowledge is available at both the transmitter and the receiver. In this work we consider the scenario in which the state is multiplied by an ergodic fading process which is not known at the encoder. We study both the case in which the receiver has knowledge of the fading and the case in which it does not: for both models we derive inner and outer bounds to capacity and determine the distance between the two bounds when possible. For the channel without fading knowledge at either the transmitter or the receiver, the gap between inner and outer bounds is finite for a class of fading distributions which includes a number of canonical fading models. In the capacity approaching strategy for this class, the transmitter performs Costa`s pre-coding against the mean value of the fading times the state while the receiver treats the remaining signal as noise. For the case in which only the receiver has knowledge of the fading, we determine a finite gap between inner and outer bounds for two classes of discrete fading distribution. The first class of distributions is the one in which there exists a probability mass larger than one half while the second class is the one in which the fading is uniformly distributed over values that are exponentially spaced apart. Unfortunately, the capacity in the case of a continuous fading distribution remains very hard to characterize

Asynchronous Joint Source-Channel Communication: An Information-Theoretic Perspective

Due to the increasing growth and demand for wireless communication services, new techniques and paradigms are required for the development of next generation systems and networks. As a first step to better differentiate between various options to develop future systems, one should consider fundamental theoretical problems and limitations in present systems and networks. Hence, some common ground between network information theory and mobile/wireless medium techniques should be explicitly addressed to better understand future generation trends. Among practical limitations, a major challenge, which is inherent and due to the physics of many mobile/wireless setups, is the problem of asynchronism between different nodes and/or clients in a wireless network. Although analytically convenient, the assumption of full synchronization between the end terminals in a network is usually difficult to justify. Thus, finding fundamental limits for communication systems under different types of asynchronism is essential to tackle real world problems. In this thesis, we study information theoretic limits that various multiuser wireless communication systems encounter under time or phase asynchronism between different nodes. In particular, we divide our research into two categories: phase asynchronous and time asynchronous systems. In the first part of this thesis, we consider several multiuser networks with phase fading communication links, i.e., all of the channels introduce phase shifts to the transmitted signals. We assume that the phase shifts are unknown to the transmitters as a practical assumption which results in a phase asynchronism between transmitter sides and receiver sides. We refer to these communication systems as phase incoherent (PI) communication systems and study the problem of communicating arbitrarily correlated sources over them. Specifically, we are interested in solving the general problem of joint source-channel coding over PI networks. To this end, we first present a lemma which is very useful in deriving necessary conditions for reliable communication of the sources over PI channels. Then, for each channel and under specific gain conditions, we derive sufficient conditions based on separate source and channel coding and show that the necessary and sufficient conditions match. Therefore, we are able to present and prove several separation theorems for channels under study under specific gain conditions. In the second part of this thesis, we consider time asynchronism in networks. In particular, we consider a multiple access channel with a relay as a general setup to model many wireless networks in which the transmitters are time asynchronous in the sense that they cannot operate at the same exact time. Based on the realistic assumption of a time offset between the transmitters, we again consider the problem of communicating arbitrarily correlated sources over such a time-asynchronous multiple access relay channel (TA-MARC). We first derive a general necessary condition for reliable communication. Then, by the use of separate source and channel coding and under specific gain conditions, we show that the derived sufficient conditions match with the general necessary condition for reliable communications. Consequently, we present a separation theorem for this class of networks under specific gain conditions. We then specialize our results to a two-user interference channel with time asynchronism between the encoders