Cooling Codes: Thermal-Management Coding for High-Performance Interconnects

High temperatures have dramatic negative effects on interconnect performance and, hence, numerous techniques have been proposed to reduce the power consumption of on-chip buses. However, existing methods fall short of fully addressing the thermal challenges posed by high-performance interconnects. In this paper, we introduce new efficient coding schemes that make it possible to directly control the <italic>peak temperature</italic> of a bus by effectively cooling its hottest wires. This is achieved by avoiding state transitions on the hottest wires for as long as necessary until their temperature drops off. We also reduce the <italic>average power consumption</italic> by making sure that the total number of state transitions on all the wires is below a prescribed threshold. We show how each of these two features can be coded for separately or, alternatively, how both can be achieved at the same time. In addition, <italic>error-correction</italic> for the transmitted information can be provided while controlling the peak temperature and/or the average power consumption. In general, our cooling codes use <inline-formula> <tex-math notation="LaTeX">$n > k$ </tex-math></inline-formula> wires to encode a given <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-bit bus. One of our goals herein is to determine the minimum possible number of wires <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> needed to encode <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> bits while satisfying any combination of the three desired properties. We provide full theoretical analysis in each case. In particular, we show that <inline-formula> <tex-math notation="LaTeX">$n = k+t+1$ </tex-math></inline-formula> suffices to cool the <inline-formula> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> hottest wires, and this is the best possibility. Moreover, although the proposed coding schemes make use of sophisticated tools from combinatorics, discrete geometry, linear algebra, and coding theory, the resulting encoders and decoders are fully practical. They do not require significant computational overhead and can be implemented without sacrificing a large circuit area.