Improved bounds for constant-power and low-power error-correcting cooling codes

Source abstract

Low-power error-correcting cooling (LPECC) codes and constant-power error-correcting cooling (CPECC) codes provide error correction while controlling power consumption and thermal effects in on-chip buses. In this paper, we study binary CPECC and LPECC codes with $e=w-3$. For CPECC codes, we extend the applicability of the upper bound previously obtained by Zhao and Zhang from the quadratic-order condition $w\ge 2t(t+1)+2$ to $w\ge w_0(t)$, where $w_0(t)\sim \sqrt{2}\,t^{3/2}$. Using Steiner systems, we show that the CPECC bound is attainable and asymptotically tight for fixed $t,w$. For LPECC codes, we establish the new upper bound $\left\lfloor\frac{\binom{n+2}{3}}{\binom{w+t}{3}}\right\rfloor$ for $w\ge μ(t)$, where $μ(t)\sim \sqrt{2}\,t^{3/2}$. This bound is strictly smaller than the previous bound of Zhao and Zhang whenever both apply, and is asymptotically tight for fixed $t,w$ in the stated range.