恒定功率和低功率纠错冷却码的改进界
Improved bounds for constant-power and low-power error-correcting cooling codes
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- State Key Laboratory of Cryptography and Digital Economy Security（密码学与数字经济安全国家重点实验室）
- Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education（教育部密码技术与信息安全重点实验室）
- School of Cyber Science and Technology, Shandong University（山东大学网络空间科学学院）
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中文总结 AI 辅助
本文改进了恒定功率和低功率纠错冷却码的上界，将适用条件从二次阶推广到 \\(t^{3/2}\\) 阶，并证明新界在固定参数下渐近紧，优于先前结果。
中文摘要 AI 辅助
低功率纠错冷却（LPECC）码和恒定功率纠错冷却（CPECC）码在控制片上总线功耗和热效应的同时提供纠错能力。本文研究了参数满足 \\(e=w-3\\) 的二元 CPECC 码和 LPECC 码。对于 CPECC 码，我们将 Zhao 和 Zhang 先前得到的上界从二次阶条件 \\(w\ge 2t(t+1)+2\\) 推广到 \\(w\ge w_0(t)\\)，其中 \\(w_0(t)\sim \sqrt{2}\\,t^{3/2}\\)。利用 Steiner 系统，我们证明了 CPECC 界在固定 \\(t,w\\) 时是可达到的且渐近紧的。对于 LPECC 码，我们建立了新的上界 \\(\left\lfloor\frac{\binom{n+2}{3}}{\binom{w+t}{3}}\right\rfloor\\)，适用于 \\(w\ge \mu(t)\\)，其中 \\(\mu(t)\sim \sqrt{2}\\,t^{3/2}\\)。该界在两者均适用时严格小于 Zhao 和 Zhang 先前的界，并且在所述范围内对固定 \\(t,w\\) 是渐近紧的。
英文摘要
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.
