Year: 2025
Type: article
Abstract: 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 overnwires that avoids state transitions on the t hottest wires and allows at most w state transitions in each transmission, and can correct up toetransmission errors. In this paper, we study the maximum possible size of an (n, t,w, e)-LPECC code, denoted byC(n, t,w, e). Whenw = e+ 2 is large, we establish a general upper boundC(n, t,w,w− 2) ≤ ⌊ (n+1 2) / (w+t2) ⌋; whenw = e+ 2 = 3, we proveC(n, t, 3, 1) ≤ ⌊n(n+1) 6(t+1) ⌋. Both bounds are tight for largensatisfying some divisibility conditions. Previously, tight bounds were known only forw = e+ 2 = 3, 4 andt≤ 2. In general, whenw = e + dis large for a constantd, we determine the asymptotic value ofC(n, t,w,w−d) ∼ (n d) / (w+t d) asngoes to infinity, which can be extended toq-ary codes.
Authors: Yuhao Zhao, Xiande Zhang
Institution: University of Science and Technology of China
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409762726