Practical coding schemes for bandwidth limited one-way communication resource allocation

This paper investigates resource allocation algorithms that use limited communication - where the supplier of a resource broadcasts a coordinating signal using one bit of information to users per iteration. Rather than relay anticipated consumption to the supplier, the users locally compute their allocation, while the supplier measures the total resource consumption. Since the users do not compare their local consumption against the supplier's capacity at each iteration, they can easily overload the system and cause an outage (for example blackout in power networks). To address this challenge, this paper investigates pragmatic coding schemes, called PF-acodes (Primal-Feasible codes), that not only allow the restriction of communication to a single bit of information, but also avoid system overload due to users' heavy consumption. We derive a worst case lower bound on the number of bits needed to achieve any desired accuracy using PF-codes. In addition, we demonstrate how to construct time-invariant and time-varying PF-codes. We provide an upper bound on the number of bits needed to achieve any desired solution accuracy using time-invariant PF-codes. Remarkably, the difference between the upper and lower bound is only 2 bits. It is proved that the time-varying PF-codes asymptotically converge to the true primal/dual optimal solution. Simulations demonstrating accuracy of our theoretical analyses are presented.