Achievable bounds on signal transition activity

Transitions on high capacitance busses in VLSI systems result in considerable system power dissipation. Therefore, various coding schemes have been proposed in the literature to encode the input signal in order to reduce the number of transitions. In this paper we derive achievable lower and upper bounds on the expected signal transition activity. These bounds are derived via an information-theoretic approach in which symbols generated by a source (possibly correlated) with entropy rate H are coded with an average of R bits/symbol. These results are applied to, 1.) determine the activity reducing efficiency of different coding algorithms such as Entropy coding, Transition coding, and Bus-Invert coding, 2.) bound the error in entropy-based power estimation schemes, and 3.) determine the lower-bound on the power-delay product. Two examples are provided where transition activity within 4% and 8% of the lower bound is achieved when blocks of 8 and 13 symbols respectively are coded at a time.