Finite-state Markov modeling of fading channels - a survey of principles and applications <s> THE FSMC MODEL <s> Communication Systems and Information Theory. A Measure of Information. Coding for Discrete Sources. Discrete Memoryless Channels and Capacity. The Noisy-Channel Coding Theorem. Techniques for Coding and Decoding. Memoryless Channels with Discrete Time. Waveform Channels. Source Coding with a Fidelity Criterion. Index. <s> BIB001 </s> Finite-state Markov modeling of fading channels - a survey of principles and applications <s> THE FSMC MODEL <s> The classical Blahut-Arimoto algorithm (BAA) is a well-known algorithm that optimizes a discrete memoryless source (DMS) at the input of a discrete memoryless channel (DMC) in order to maximize the mutual information between channel input and output. This paper considers the problem of optimizing finite-state machine sources (FSMSs) at the input of finite-state machine channels (FSMCs) in order to maximize the mutual information rate between channel input and output. Our main result is an algorithm that efficiently solves this problem numerically; thus, we call the proposed procedure the generalized BAA. It includes as special cases not only the classical BAA but also an algorithm that solves the problem of finding the capacity-achieving input distribution for finite-state channels with no noise. While we present theorems that characterize the local behavior of the generalized BAA, there are still open questions concerning its global behavior; these open questions are addressed by some conjectures at the end of the paper. Apart from these algorithmic issues, our results lead to insights regarding the local conditions that the information-rate-maximizing FSMSs fulfill; these observations naturally generalize the well-known Kuhn-Tucker conditions that are fulfilled by capacity-achieving DMSs at the input of DMCs. <s> BIB002
We introduce data-independent FSMC models, in which the channel input and channel state are statistically independent. This class of FSMC models is more suitable for modeling the TV-FFC, where the fading channel gain h and the channel input x are independent of each other. The general definition of FSMC models, including data-dependent FSMC models can be found in BIB001 and BIB002 . Figure 5 shows a snapshot of an FSMC model with K = 4 states and its evolution in N = 4 time samples. Assume that at first time step, the channel is in state s = 0. In this state, the channel acts like a binary symmetric channel (BSC). Let us denote the binary input, output, and error in the BSC by x, y, and z, respectively, where y x ⊕ z and ⊕ denotes addition in modulo two. The error probability in the first BSC is P e0 Pr(Z = 1|S = 0). Let us assume that at the first time step, x = 1 was sent and an error z = 1 occurred with probability P e0 to produce the BSC output y = 0. This is highlighted in the figure. In the next time step, the channel moves to another state, say s = 3 with state transition probability equal to P 0→3 Pr(S = 3|S −1 = 0). The key feature of an FSMC model is that given the new state and input of the channel, communication through the channel is memoryless or independent of previous channel states, inputs, and outputs. For example, given that the new state of the channel is s = 3, the channel acts like a new BSC with another error probability P e3 = Pr(Z = 1|S = 3). As highlighted in the figure, we have assumed that at the second time step, x = 0 was sent and no error occurred or z = 0 with probability 1 − P e3 to produce the BSC output y = 0. This process is repeated for the future time steps.