Voronoi-Hamming Algorithms for Optimizing Channel Selection From the Radio Frequency Transmission Hypercube

Advancing and applying our recent NASA-sponsored research for deep space avionics, we propose to develop new algorithms which - provably, autonomously, and in the presence of faults i) optimize the selection of channels from the radio frequencyTransmission Hypercube, as it is termed in the OSD03-026 solicitation, in order to ii) connect healthy nodes into a working network quorum, and iii) keep them connected. To this end, we crystallize objectives for channel capacity (throughput) and latency(packet delay) in the language of optimization. Maximizing aggregate Shannon capacity (Eqns (11), (12)), our scalable algorithms will adaptively activate and deactivate channels, subject to constraints on channel bandwidth, number of channels, and per-bandlimits on signal power and noise. Similarly, and in the presence of faulty nodes and channels, our distributed algorithms will minimize latency (network radius or diameter, Eqn (1)). Where throughput and latency can be viewed as constraints, our algorithmswill also solve dual problems whose objective is to minimize consumption of channel resources, such as power (Eqn (13)). Our approach blends information theory with breakthroughs in the mathematics of connectivity, especially 1.2.6) optimal routing enabledby Hamming graphs and 1.2.7) Voronoi algorithms from computational geometry.