Capacity Region of the Finite-State Multiple-Access Channel With and Without Feedback

Dept. of Electr. & Comput. Eng., Ben-Gurion Univ. of the Negev, Beer-Sheva
IEEE Transactions on Information Theory (Impact Factor: 2.33). 07/2009; 55(6):2455 - 2477. DOI: 10.1109/TIT.2009.2018346
Source: IEEE Xplore


The capacity region of the finite-state multiple-access channel (FS-MAC) with feedback that may be an arbitrary time-invariant function of the channel output samples is considered. We characterize both an inner and an outer bound for this region, using Massey's directed information. These bounds are shown to coincide, and hence yield the capacity region, of indecomposable FS-MACs without feedback and of stationary and indecomposable FS-MACs with feedback, where the state process is not affected by the inputs. Though multiletter in general, our results yield explicit conclusions when applied to specific scenarios of interest. For example, our results allow us to do the following. 1. Identify a large class of FS-MACs, that includes the additive mod2 noise MAC where the noise may have memory, for which feedback does not enlarge the capacity region. 2. Deduce that, for a general FS-MAC with states that are not affected by the input, if the capacity (region) without feedback is zero, then so is the capacity (region) with feedback. 3. Deduce that the capacity region of a MAC that can be decomposed into a multiplexer concatenated by a point-to-point channel (with, without, or with partial feedback), the capacity region is given by Sigmam Rm les C, where C is the capacity of the point to point channel and m indexes the encoders. Moreover, we show that for this family of channels source-channel coding separation holds.

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    • "In a different line of research, the capacity region was determined by Kramer [9] in terms of directed information. Permuter et al [10] also investigated the capacity of the MAC with memory and feedback. However, these expressions are in an incomputable multi-letter form, and thus, a single-letter characterization of the capacity region for the DM-MAC with feedback is still an open problem. "
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    ABSTRACT: We consider the problem of communication over a multiple access channel (MAC) with noiseless feedback. A single-letter characterization of the capacity of this channel is not currently known in general. We formulate the MAC with feedback capacity problem as a stochastic control problem for a special class of channels for which the capacity is known to be the single-letter expression given by Cover and Leung. This approach has been recently successful in finding channel capacity for point-to-point channels with noiseless feedback but has not yet been fruitful in the study of multi-user communication systems. Our interpretation provides an understanding of the role of auxiliary random variables and can also hint at on-line capacity-achieving transmission schemes.
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    • "In particular, it was shown in [4] that feedback can increase the capacity of some FSCs. The capacity of finite-state multiple-access channels (FS-MACs) with and without feedback was also studied in a recent work [6]. The finite-state broadcast channel (FSBC) was originally introduced in [7] and [8]. "
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    • "Dabora and Goldsmith [26] found the capacity region of the discretetime , time-varying broadcast channel with memory in two different cases of feedback knowledge. Permuter et al. [27] determined the capacity region of finite-state multipleaccess channel in the presence or absence of feedback information. Finally, Tatikonda and Mitter [28] developed a general framework for channels with memory and feed- back. "
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    ABSTRACT: The goal of this paper is to investigate the effect of channel side information on increasing the achievable rates of continuous power-limited non-Gaussian channels. We focus on the case where (1) there is imperfect channel quality information available to the transmitter and the receiver and (2) while the channel gain is continuously varying, there are few cross-region changes, and the noise characteristics remain in each detection region for a long time. The results are presented for two scenarios, namely, reliable and unreliable region detection. Considering short- and long-term power constraints, the capacity bounds are found for log-normal and two different Nakagami-based channel distributions, and for both Max-Lloyd and equal probability quantization approaches. Then, the optimal gain partitioning approach, maximizing the achievable rates, is determined. Finally, general equations for the channel capacity bounds and optimal channel partitioning in the case of unreliable region detection are presented. Interestingly, the results show that, for high SNR's, it is possible to determine a power-independent optimal gain partitioning approach maximizing the capacity lower bound which, in both scenarios, is identical for both short- and long-term power constraints.
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