A digital spiking neuron is a wired system of shift registers that can generate spike-trains having various spike patterns by adjusting the wiring pattern between the registers. Inspired by the ultra-wideband impulse radio, a novel theoretical synthesis method of the neuron for application to spike-pattern division multiplex communications in an artificial pulse-coupled neural network is presented. Also, a novel heuristic learning algorithm of the neuron for realization of better communication performances is presented. In addition, fundamental comparisons to existing impulse radio sequence design methods are given.