标题： 具有大距离的低功耗纠错冷却码 显示英文标题

标题： On low-power error-correcting cooling codes with large distances

摘要： 一种低功耗纠错冷却（LPECC）码被Chee等人引入作为一种总线通信的编码方案，以同时控制峰值温度、片上总线的平均功耗和传输信息的纠错。具体而言，一个$(n, t, w, e)$-LPECC码是在$n$根线上的一种编码方案，它避免在$t$根最热的线上发生状态转换，并且每次传输中最多允许$w$次状态转换，可以纠正最多$e$次传输错误。在本文中，我们研究了$(n, t, w, e)$-LPECC码的最大可能大小，记为$C(n,t,w,e)$。 当$w=e+2$很大时，我们建立了一个一般的上界$C(n,t,w,w-2)\leq \lfloor \binom{n+1}{2}/\binom{w+t}{2}\rfloor$；当$w=e+2=3$时，我们证明了$C(n,t,3,1) \leq \lfloor \frac{n(n+1)}{6(t+1)}\rfloor$。 这两个界对于满足某些可除性条件的大$n$是紧的。 之前，仅对$w=e+2=3,4$和$t\leq 2$知道紧界。 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. 显示英文摘要

摘要： 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.