On the achievable rates in decentralized networks with Randomized Masking

We address a two-user1 decentralized interference channel with static non-frequency selective channel gains. Both users are unaware of each other's code-books and there is no central controller to manage the allocation of resources between the two users. As multiuser detection is not possible, the conventional scheme of transmitting a continuous stream of i.i.d. symbols from Gaussian codebooks by each transmitter (referred to as continuous transmission) results in excessive interference. To provide both users with a partially interference-free channel, we propose that each user randomly quits transmitting from transmission slot to transmission slot independently with a probability of 1 - ε ε ∈ (0, 1). This is called the Randomized Masking (RM) protocol. Due to the on-off nature of transmissions, the noise plus interference process has a mixed distribution. As a result, the mutual information between the input and the output of the channels does not accept any closed form expression. Assuming each user transmits i.i.d. signals upon activation, the highest achievable rate by each user is denoted by CRM-I. We derive upper and lower bounds on CRM-I where Entropy Power Inequality (EPI) and the extremal inequality of Liu and Viswanath [4] are two important tools in this analysis. Using the proposed lower bound, we devise a distributed strategy to select the activity factor e. Note that this strategy includes the conventional continuous transmission by setting ε = 1. The main result of the paper states that there exist values of 0 ≤ α <  < β ≤ 1 such that for all ε ∈ (α, β) it is possible to achieve rates larger than CRM-I as far as the Signal-to-Noise Ratio (SNR) is sufficiently large. Therefore, it is proved that transmitting i.i.d. signals in consecutive transmission slots is not optimum under the RM protocol.