Linear superposition coding for the asymmetric Gaussian MAC with quantized feedback

We propose a linear transceiver scheme for the asymmetric two-user multiple access channel with additive Gaussian noise and quantized feedback. The quantized feedback link is modeled as an information bottleneck subject to a rate constraint. We introduce a superposition scheme that splits the transmit power between an Ozarow-like linear-feedback code and a conventional code that ignores the feedback. We study the achievable sum rate as a function of the feedback quantization rate and we show that sum rate maximization leads to a difference of convex functions problem that we solve via the convex-concave procedure.

[1]  Gerald Matz,et al.  Rate-information-optimal Gaussian channel output compression , 2014, 2014 48th Annual Conference on Information Sciences and Systems (CISS).

[2]  Amos Lapidoth,et al.  On the AWGN MAC With Imperfect Feedback , 2010, IEEE Transactions on Information Theory.

[3]  G. Matz,et al.  Linear superposition coding for the Gaussian MAC with quantized feedback , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[5]  Alan L. Yuille,et al.  The Concave-Convex Procedure , 2003, Neural Computation.

[6]  Gerald Matz,et al.  The rate-information trade-off for Gaussian vector channels , 2014, 2014 IEEE International Symposium on Information Theory.

[7]  J. Pieter M. Schalkwijk,et al.  A coding scheme for additive noise channels with feedback-II: Band-limited signals , 1966, IEEE Trans. Inf. Theory.

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

[9]  Gerald Matz,et al.  On the relation between the Gaussian information bottleneck and MSE-optimal rate-distortion quantization , 2014, 2014 IEEE Workshop on Statistical Signal Processing (SSP).

[10]  Stephen P. Boyd,et al.  Variations and extension of the convex–concave procedure , 2016 .

[11]  G. Kramer,et al.  On Cooperation Via Noisy Feedback , 2006, 2006 International Zurich Seminar on Communications.

[12]  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.

[13]  Naftali Tishby,et al.  The information bottleneck method , 2000, ArXiv.

[14]  Gal Chechik,et al.  Information Bottleneck for Gaussian Variables , 2003, J. Mach. Learn. Res..