Entropic bounds on FSM switching

Several state assignment algorithms have attempted to minimize the average Hamming distance per transition in the hopes of generating low power assignments. There has not been a reasonable theoretical lower bound on the average Hamming distance per transition that is applicable to every state assignment for a given finite state machine (FSM). Such a lower bound serves many roles-a target for algorithm designers, provides clues about what types of FSM structures are likely to have low average switching per transition, could be incorporated into a high-level power model. We provide two such lower bounds which were also found to be achievable empirically within 17% for MCNC benchmarks. An interesting byproduct of one of these 'theoretical' lower bounds was a greedy state assignment algorithm which is amenable to a very distributed (parallel) implementation. This algorithm also outperforms JEDI by 2.5% for area and by 21% for power over MCNC benchmarks.