A low-power error-correcting cooling (LPECC) code was introduced as a coding scheme for communication over a bus by Chee et al. to control the peak temperature, the average power consumption of on-chip buses, and error-correction for the transmitted information, simultaneously. Specifically, an $(n, t, w, e)$-LPECC code is a coding scheme over $n$ wires that avoids state transitions on the $t$ hottest wires and allows at most $w$ state transitions in each transmission, and can correct up to $e$ transmission errors. In this paper, we study the maximum possible size of an $(n, t, w, e)$-LPECC code, denoted by $C(n,t,w,e)$. When $w=e+2$ is large, we establish a general upper bound $C(n,t,w,w-2)\leq \lfloor \binom{n+1}{2}/\binom{w+t}{2}\rfloor$; when $w=e+2=3$, we prove $C(n,t,3,1) \leq \lfloor \frac{n(n+1)}{6(t+1)}\rfloor$. Both bounds are tight for large $n$ satisfying some divisibility conditions. Previously, tight bounds were known only for $w=e+2=3,4$ and $t\leq 2$. In general, when $w=e+d$ is large for a constant $d$, we determine the asymptotic value of $C(n,t,w,w-d)\sim \binom{n}{d}/\binom{w+t}{d}$ as $n$ goes to infinity, which can be extended to $q$-ary codes.

翻译：低功耗纠错冷却（LPECC）码由Chee等人提出，作为一种用于总线通信的编码方案，旨在同时控制峰值温度、片上总线的平均功耗以及对传输信息的纠错。具体而言，一个$(n, t, w, e)$-LPECC码是在$n$条线路上的一种编码方案，它避免在最热的$t$条线路上发生状态转换，允许每次传输中最多发生$w$次状态转换，并且能够纠正最多$e$个传输错误。本文研究了$(n, t, w, e)$-LPECC码的最大可能尺寸，记为$C(n,t,w,e)$。当$w=e+2$较大时，我们建立了一个通用上界$C(n,t,w,w-2)\leq \lfloor \binom{n+1}{2}/\binom{w+t}{2}\rfloor$；当$w=e+2=3$时，我们证明了$C(n,t,3,1) \leq \lfloor \frac{n(n+1)}{6(t+1)}\rfloor$。对于满足某些整除条件的大$n$，这两个界都是紧的。此前，紧界仅在$w=e+2=3,4$且$t\leq 2$的情况下已知。一般而言，当$w=e+d$对于常数$d$较大时，我们确定了当$n$趋于无穷时$C(n,t,w,w-d)\sim \binom{n}{d}/\binom{w+t}{d}$的渐近值，该结果可推广至$q$元码。