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Abstract-In this paper we consider the feedback capacity of a class of symmetric finite-state Markov channels. For this type of channels, symmetry is a generalized version of the symmetry defined for discrete memoryless channels. We show that feedback does not increase capacity for such class of finite-state channels. We indeed demonstrate that for such channels, both non-feedback and feedback capacities are achieved by a uniform i.i.d. input distribution.

We consider the problem of reliable communication over multiple-access channels (MAC) where the channel is driven by an independent and identically distributed state process and the encoders and the decoder are provided with various degrees of asymmetric noisy channel state information (CSI). For the case where the encoders observe causal, asymmetric noisy CSI and the decoder observes complete CSI, we provide inner and outer bounds to the capacity region, which are tight for the sum-rate capacity. We then observe that, under a Markov assumption, similar capacity results also hold in the case where the receiver observes noisy CSI. Furthermore, we provide a single letter characterization for the capacity region when the CSI at the encoders are asymmetric deterministic functions of the CSI at the decoder and the encoders have non-causal noisy CSI (its causal version is recently solved in [1]). When the encoders observe asymmetric noisy CSI with asymmetric delays and the decoder observes complete CSI, we provide a single letter characterization for the capacity region. Finally, we consider a cooperative scenario with common and private messages, with asymmetric noisy CSI at the encoders and complete CSI at the decoder. We provide a single letter expression for the capacity region for such channels.For the cooperative scenario, we also note that as soon as the common message encoder does not have access to CSI, then in any noisy setup, covering the cases where no CSI or noisy CSI at the decoder, it is possible to obtain a single letter characterization for the capacity region. The main component in these results is a generalization of a converse coding approach, recently introduced in [1] for the MAC with asymmetric quantized CSI at the encoders and herein considerably extended and adapted for the noisy CSI setup. DRAFT [20] and [21]. Finally, for a comprehensive survey on channel coding with side information see [22].The most relevant work to this paper is [1], which presents a single letter characterization of the capacity region for memoryless FS-MAC in which transmitters observe asymmetric partial quantized CSI causally, and the receiver has full CSI. In the converse part of this work, which we discuss in more detail below, the authors use team decision theoretic methods [23] (see also [24], [25] and [26] for recent team decision and control theoretic approaches). When a comparison of this result with the previously mentioned results is made, we observe the following: i) it shows that when the state process is i.i.d. there is no loss of optimality if the encoders use a window size of k = 1 in [11, Theorem 3], ii) it extends the causal part of result [12, Theorem 5] to the case where CSITs are not independent, and finally, iii) it partially answers the setup in [13, Theorem 2] with the assumption that CSITs are causal. September 4, 2018 DRAFT 4 A. Main Contributions and Connections with the LiteratureWe consider several scenarios where the encoders and the decoder observe various degrees of noisy CSI. The essenti...

Abstract-A single-letter characterization is provided for the capacity region of finite-state multiple-access channels, when the channel state process is an independent and identically distributed sequence, the transmitters have access to partial (quantized) state information, and complete channel state information is available at the receiver. The partial channel state information is assumed to be asymmetric at the encoders. As a main contribution, a tight converse coding theorem is presented. The difficulties associated with the case when the channel state has memory are discussed and connections to decentralized stochastic control theory are presented.Index Terms-Asymmetric channel state information, decentralized stochastic control, multiple-access channel, nonnested information structure.

Mean field game (MFG) theory where there is a major player and many minor players (MM-MFG) has been recently introduced in both the linear quadratic Gaussian (LQG) case and in the case of nonlinear state dynamics and nonlinear cost functions. In this framework, a major player has a significant influence, i.e., asymptotically non-vanishing, on any minor agent. In contrast to the situation without major agents, the mean field term now becomes stochastic due to the stochastic evolution of the state of the major player and, as a result, the best response control actions of the minor agents depend on the state of the major agent as well as the stochastic mean field. In a decentralized environment, one is led to consider the situation where the agents are provided only with partial information on the major agent's state and the mean field term. In this work, we consider such a scenario for systems with nonlinear dynamics and cost functions and develop MFG theory for a partially observed MM-MFG setup. More explicitly, we consider a MFG problem with (i) partial observations on the major player state provided to the minor agents individually and (ii) complete observations on that state provided to the major player. The first step of such a theory requires one to develop an estimation theory for partially observed stochastic dynamical systems whose state equations are of McKean-Vlasov (MV) type stochastic differential equations. The next approach to the problem for MM-MFG systems in this work is to follow the procedure of constructing the associated completely observed system via the application of nonlinear filtering theory. The existence and uniqueness of Nash equilibria is then analyzed in this setting.