Symmetric decentralized interference channels with noisy feedback

Decentralized interference channels with noisy feedback possess Pareto optimal Nash equilibria

“…2) of the symmetric LD-DIC with noisy feedback with parameters − → n , ← − n and m is given by Theorem 1 in [3]. Let N ( − → n , ← − n ,m) denote such an NE region and consider the following region:…”

“…Corollary 1 leads to an interesting upper bound for the PoA in the very weak interference regime: 1 PoA (G) 3 2 . Note that no loss in the sum rate is observed due to the anarchical behavior of the players (PoA (G) = 1) when the signal to noise ratios (SNRs) of the feedback links are lower than the signal to interference ratios (SIRs) of the direct links, i.e., β 1 − α (see Fig.…”

“…This is explained by the fact that under these conditions, α 1 2 and β 1 − α, the Nash regions with and without feedback links are identical and thus, the unique rate pair achievable at an NE, which is achieved by treating interference as noise, falls on the boundary of the capacity region [1], [2]. Alternatively, when the SNRs of the feedback links are higher than the SIRs of the direct links β 1 − α, the use of feedback enlarges the NE region and thus, treating interference as noise becomes the worse NE [3]. Therefore, it follows that PoA (G) > 1 (see Fig.…”

“…1). The upperbound PoA (G) 3 2 follows from the fact that increasing the SNRs of the feedback links beyond the SIRs of the direct links does not push forward the sum-rate upper bounds of the capacity region [3] and for all α 1 2 , it follows that 2−α 2(1−α) 3 2 (see Fig. 1).…”

“…Even in the case of noisy feedback, these benefits have been shown to be very relevant. For instance, the set of achievable rate pairs at a Nash equilibrium (NE), also known as the Nash region, has been shown to be enlarged, in most of the cases, thanks to the use of feedback despite the existence of noise [3].…”