Article

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: 2.65). 07/2009; DOI: 10.1109/TIT.2009.2018346
Source: IEEE Xplore

ABSTRACT 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 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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    ABSTRACT: In this paper, we consider the discrete, time-varying broadcast channel (BC) with memory under the assumption that the channel states belong to a set of finite cardinality. We study the achievable rates in several scenarios of feedback and full unidirectional receiver cooperation. In particular, we focus on two scenarios: the first scenario is the general finite-state broadcast channel (FSBC) where both receivers send feedback to the transmitter while one receiver also sends its channel output to the second receiver. The second scenario is the degraded FSBC where only the strong receiver sends feedback to the transmitter. Using a superposition codebook construction, we derive the capacity regions for both scenarios. Combining elements from these two basic results, we obtain the capacity regions for a number of additional broadcast scenarios with feedback and unidirectional receiver cooperation.
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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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    • "q on the channel inputs. We also define the following quantities, see also [6, Section II.C], [4], [7]: "
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    ABSTRACT: We study the capacity of indecomposable finite-state channels (FSCs) with feedback. In this class of channels, the effect of the initial state on the state transition probabilities for every given input sequence becomes negligible as time evolves. It is known that for indecomposable FSCs without feedback the capacity is independent of the initial state. Similar results were obtained for indecomposable finite-state multiple access channels and indecomposable degraded finite-state broadcast channels. However, when feedback is present, such a result does not exist except for FSCs without intersymbol interference (ISI). In this paper we show that the capacity-achieving distribution of indecomposable FSCs with feedback can be computed without minimizing over all initial channel states.
    Communication, Control, and Computing, 2008 46th Annual Allerton Conference on; 10/2008

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