Approximated Capacity of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback

In this research report, an achievability region and a converse region for the two-user Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits. Key-words: Achievable region, converse region, two-user Gaussian interference channel, noisy chanel-output feedback Victor Quintero, Samir M. Perlaza and Jean-Marie Gorce are with the CITI Laboratory of the Institut National de Recherche en Informatique et en Automatique (INRIA), Université de Lyon, and Institut National de Sciences Apliquées (INSA) de Lyon. 6 Av. des Arts 69621 Villeurbanne, France. ({victor.quintero-florez, samir.perlaza, jean-marie.gorce}@inria.fr). Iñaki Esnaola is with the Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, United Kingdom. (esnaola@sheffield.ac.uk). Victor Quintero is also with Universidad del Cauca, Popayán, Colombia. Samir M. Perlaza and Iñaki Esnaola are also with the Department of Electrical Engineering at Princeton University, Princeton, NJ. This research was supported in part by the European Commission under Marie Sklodowska-Curie Individual Fellowship No. 659316 (CYBERNETS); and the Administrative Department of Science, Technology, and Innovation of Colombia (Colciencias), fellowship No. 617-2013. Parts of this work were presented at the IEEE International Workshop on Information Theory (ITW), Cambridge, United Kingdom, September, 2016. This work was also submitted to the IEEE Transactions on Information Theory in November 1