The Gaussian channel with noisy feedback: improving reliability via interaction

Consider a pair of terminals connected by two independent (feedforward and feedback) Additive White Gaussian Noise (AWGN) channels, and limited by individual power constraints. The first terminal would like to reliably send information to the second terminal at a given rate. While the reliability in the cases of no feedback and of noiseless feedback is well studied, not much is known about the case of noisy feedback. In this work, we present an interactive scheme that significantly improves the reliability relative to the no-feedback setting, whenever the feedback Signal to Noise Ratio (SNR) is sufficiently larger than the feedforward SNR. The scheme combines Schalkwijk-Kailath (S-K) coding and modulo-lattice analog transmission.

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

[2]  Tsachy Weissman,et al.  The Gaussian Channel with Noisy Feedback , 2007, 2007 IEEE International Symposium on Information Theory.

[3]  Aaron D. Wyner,et al.  The rate-distortion function for source coding with side information at the decoder , 1976, IEEE Trans. Inf. Theory.

[4]  J. Wolfowitz.  The rate distortion function for source coding with side information at the decoder , 1979 .

[5]  Thomas J. Goblick,et al.  Theoretical limitations on the transmission of data from analog sources , 1965, IEEE Trans. Inf. Theory.

[6]  Tsachy Weissman,et al.  On the Reliability of Gaussian Channels with Noisy Feedback , 2007 .

[7]  R. Gallager.  Information Theory and Reliable Communication , 1968 .

[8]  J. Wolfowitz.  The rate distortion function for source coding with side information at the decoder. II , 1979 .

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

[10]  Meir Feder,et al.  Optimal Feedback Communication Via Posterior Matching , 2009, IEEE Transactions on Information Theory.

[11]  Simon Litsyn,et al.  Lattices which are good for (almost) everything , 2005, IEEE Transactions on Information Theory.

[12]  C. Shannon.  Probability of error for optimal codes in a Gaussian channel , 1959 .

[13]  Michael Horstein,et al.  Sequential transmission using noiseless feedback , 1963, IEEE Trans. Inf. Theory.

[14]  Yuval Kochman,et al.  Joint Wyner–Ziv/Dirty-Paper Coding by Modulo-Lattice Modulation , 2008, IEEE Transactions on Information Theory.

[15]  Assaf Ben-Yishai,et al.  The Gaussian channel with noisy feedback: Near-capacity performance via simple interaction , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  Yuval Kochman,et al.  Lattice Coding for Signals and Networks: Lattice shaping , 2014 .

[17]  Hirosuke Yamamoto,et al.  Noisy feedback improves the Gaussian channel reliability function , 2014, 2014 IEEE International Symposium on Information Theory.

[18]  Yuval Kochman,et al.  Joint Wyner-Ziv / Dirty-Paper Coding by Analog Modulo-Lattice Modulation † , 2009 .