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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    ABSTRACT: In this paper, we derive the capacity regions of a continuous-time white Gaussian multiple access channel with/without feedback, a continuous-time white Gaussian interference channel without feedback and a continuous-time white Gaussian broadcast channel without feedback. These "complete" results stand in stark contrast to the status quo of network information theory in discrete-time, where the capacity regions of the all the above-mentioned channels are known only for a handful of special scenarios.
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    ABSTRACT: A single-letter characterization is provided for the capacity region of finite-state multiple access channels using directed information. The channel state is a Markov process, the transmitters have access to delayed state information, and channel state information is available at the receiver. The delays of the channel state information are assumed to be asymmetric at the transmitters. We obtain the capacity region by innovative way, using a multi-letter expression for the capacity region of finite-state MAC with time-invariant feedback. Index Terms—Capacity region, Delayed feedback, Directed informa- tion, Finite-state channel, Multiple-Access channel.
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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.
    Communications (ICC), 2012 IEEE International Conference on; 01/2012


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