On the Capacity of Multiple Access Channels with State Information and Feedback

In this paper, the multiple access channel (MAC) with channel state is analyzed in a scenario where a) the channel state is known non-causally to the transmitters and b) there is perfect causal feedback from the receiver to the transmitters. An achievable region and an outer bound are found for a discrete memoryless MAC that extend existing results, bringing together ideas from the two separate domains of MAC with state and MAC with feedback. Although this achievable region does not match the outer bound in general, special cases where they meet are identified. In the case of a Gaussian MAC, a specialized achievable region is found by using a combination of dirty paper coding and a generalization of the Schalkwijk-Kailath, Ozarow and Merhav-Weissman schemes, and this region is found to be capacity achieving. Specifically, it is shown that additive Gaussian interference that is known non-causally to the transmitter causes no loss in capacity for the Gaussian MAC with feedback.

[1]  Thomas Kailath,et al.  A coding scheme for additive noise channels with feedback-I: No bandwidth constraint , 1966, IEEE Trans. Inf. Theory.

[2]  Frans M. J. Willems,et al.  The discrete memoryless multiple-access channel with cribbing encoders , 1985, IEEE Trans. Inf. Theory.

[3]  Claude E. Shannon,et al.  The zero error capacity of a noisy channel , 1956, IRE Trans. Inf. Theory.

[4]  Federico Kuhlmann,et al.  Achievability proof of some multiuser channel coding theorems using backward decoding , 1989, IEEE Trans. Inf. Theory.

[5]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[6]  Claude E. Shannon,et al.  Channels with Side Information at the Transmitter , 1958, IBM J. Res. Dev..

[7]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[8]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[9]  Abbas El Gamal,et al.  On the capacity of computer memory with defects , 1983, IEEE Trans. Inf. Theory.

[10]  Lawrence H. Ozarow,et al.  An achievable region and outer bound for the Gaussian broadcast channel with feedback , 1984, IEEE Trans. Inf. Theory.

[11]  Jack K. Wolf,et al.  The capacity region of a multiple-access discrete memoryless channel can increase with feedback (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[12]  Tsachy Weissman,et al.  Coding for the feedback Gel'fand-Pinsker channel and the feedforward Wyner-Ziv source , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[13]  Michael Gastpar,et al.  Boosting reliability over AWGN networks with average power constraints and noiseless feedback , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[14]  T. Kailath,et al.  A coding scheme for additive noise channels with feedback, Part I: No bandwith constraint , 1998 .

[15]  Gerhard Kramer,et al.  Feedback strategies for white Gaussian interference networks , 2002, IEEE Trans. Inf. Theory.

[16]  Young-Han Kim,et al.  Multiple user writing on dirty paper , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[17]  Cyril Leung,et al.  An achievable rate region for the multiple-access channel with feedback , 1981, IEEE Trans. Inf. Theory.

[18]  Tsachy Weissman,et al.  Coding for the feedback Gel'fand-Pinsker channel and the feedforward Wyner-Ziv source , 2005, ISIT.

[19]  Nicola Elia,et al.  When bode meets shannon: control-oriented feedback communication schemes , 2004, IEEE Transactions on Automatic Control.

[20]  Lawrence H. Ozarow,et al.  The capacity of the white Gaussian multiple access channel with feedback , 1984, IEEE Trans. Inf. Theory.