In late 1950s and early 1960s, Gilbert and Elliott at Bell Labs were modeling burst-noise telephone circuits with a very simple two-state channel model with memory. This simple model allowed them to evaluate channel capacity and error rate performance through bursty wireline telephone circuits. However, it took another 30 years for the so-called Gilbert-Elliott channel (GEC) and its generalized finite-state Markov channel (FSMC) to be applied in the design of second-generation (2G) wireless communication systems. Since the mid 1990s, the GEC and FSMC models have been widely used for modeling wireless flat-fading channels in a variety of applications, ranging from modeling channel error bursts to decoding at the receiver. FSMC models are versatile, and with suitable choices of model parameters, can capture the essence of time-varying fading channels. This article's goal is to provide an in-depth understanding of the principles of FSMC modeling of fading channels with its applications in wireless communication systems. Digital Object Identifier 10.1109/MSP.2008 [ Parastoo Sadeghi, Rodney A. Kennedy, Predrag B. Rapajic, and Ramtin Shams ] While the emphasis is on frequency nonselective or flat-fading channels, this understanding will be useful for future generalizations of FSMC models for frequency-selective fading channels. The target audience of this article include both theory-and practice-oriented researchers who would like to design accurate channel models for evaluating the performance of wireless communication systems in the physical or media access control layers, or those who would like to develop more efficient and reliable transceivers that take advantage of the inherent memory in fading channels. Both FSMC models and flat-fading channels will be formally introduced. However, a background in time-varying fading communication channels is beneficial.We consider the FSMC modeling of fading channels from five distinct viewpoints. First, we provide a brief history of FSMC models and the FSMC modeling of flat-fading channels. Second, we define the parameters of FSMC models and discuss how these parameters can be derived from flat-fading channel statistics. We point out the trade-offs between model accuracy and complexity. Third, we categorize applications of FSMC models for fading channels into four categories and discuss the FSMC model applicability and accuracy in each application. We pay special attention to the effect of FSMC memory order on the model accuracy. Fourth, we consider the information-theoretical aspects of FSMC models and the FSMC modeling of fading channels. Finally, we present open questions and directions for future research. For easier access to the technical contents, the reader can refer to the "List of Acronyms" and "Notational Conventions." THE HISTORY OF FSMC 1957-1968: DEVELOPMENT OF FSMC MODELSThe study of finite-state communication channels with memory dates back to the work by Shannon in 1957 [1]. In [1], Shannon proved coding theorems for finite-state channels (FSCs) with discret...

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We consider the issues of cost and fairness in the problem of cooperative data exchange among a group of wireless clients. In this problem, each client initially holds a subset of packets and needs to obtain the full set of packets through cooperation with other clients via a shared broadcast channel. To find minimum cost transmission schemes, we propose a general model for the problem which is based on network information flow with side information available to the sinks. As a special case of minimum cost solutions, the minimum number of required transmissions is studied in detail. We show that packet splitting is a natural consequence of solving the linear programming associated with the mentioned network flow problem. Our main observation is that splitting the packets not only minimizes the number of transmissions, but also it results in considerably more fairness compared to the case where splitting is not allowed. Hence, incentive-based long-term cooperation among users can be sustained.

We consider the problem of minimizing upper bounds and maximizing lower bounds on information rates of stationary and ergodic discrete-time channels with memory. The channels we consider can have a finite number of states, such as partial response channels, or they can have an infinite state-space, such as time-varying fading channels.We optimize recently-proposed information rate bounds for such channels, which make use of auxiliary finite-state machine channels (FSMCs). Our main contribution in this paper is to provide iterative expectationmaximization (EM) type algorithms to optimize the parameters of the auxiliary FSMC to tighten these bounds.We provide an explicit, iterative algorithm that improves the upper bound at each iteration. We also provide an effective method for iteratively optimizing the lower bound. To demonstrate the effectiveness of our algorithms, we provide several examples of partial response and fading channels, where the proposed optimization techniques significantly tighten the initial upper and lower bounds. Finally, we compare our results with an improved variation of the simplex local optimization algorithm, called Soblex. This comparison shows that our proposed algorithms are superior to the Soblex method, both in terms of robustness in finding the tightest bounds and in computational efficiency.Interestingly, from a channel coding/decoding perspective, optimizing the lower bound is related to increasing the achievable mismatched information rate, i.e., the information rate of a communication system where the decoder at the receiver is matched to the auxiliary channel, and not to the original channel.