恒功率/低功率纠错冷却码的界与构造
Bounds and constructions for constant/low-power error-correcting cooling codes
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中文总结 AI 辅助
本文针对恒功率/低功率纠错冷却码，利用图论、组合构型、概率方法推导新上界、构造最优码族，解决相关猜想并建立两类最优码间关系。
中文摘要 AI 辅助
低功率纠错冷却（LPECC）码和恒功率纠错冷却（CPECC）码分别于文献[IEEE Trans. Inf. Theory, 64 (2018), 3062--3085; 66 (2020), 4804--4818]中提出，是两类编码方案，旨在同时控制片上总线的峰值温度与平均功耗，为传输信息提供纠错能力。本文利用图论技术建立了$(n,1,w,w-2)$-CPECC码和$(n,t,w,w-2)$-CPECC码的新上界，通过组合构型构造了多个新的最优CPECC码族，完全解决了文献[IEEE Trans. Inf. Theory, DOI: https://doi.org/10.1109/TIT.2026.3721101]中提出的关于CPECC码的猜想；此外，本文利用概率方法推导了$(n,t,w,w-2)$-LPECC码的新上界，构造了新的最优码族，并建立了最优$(n,t,w,w-2)$-LPECC码与最优$(n+1,t,w,w-2)$-CPECC码之间的关系。
英文摘要
The low-power error-correcting cooling (LPECC) codes and constant-power error-correcting cooling (CPECC) codes, introduced in [IEEE Trans. Inf. Theory, 64 (2018), 3062--3085; 66 (2020), 4804--4818], respectively, are two coding schemes designed to simultaneously control the peak temperature and average power consumption of on-chip buses while providing error-correction capability for transmitted information. This paper establishes new upper bounds for both $(n,1,w,w-2)$-CPECC codes and $(n,t,w,w-2)$-CPECC codes using graph-theoretic techniques, and constructs several new families of optimal CPECC codes using combinatorial configurations. Moreover, it completely resolves the conjecture concerning CPECC codes posed in [IEEE Trans. Inf. Theory, DOI: 10.1109/TIT.2026.3721101]. Finally, we derive a new upper bound for $(n,t,w,w-2)$-LPECC codes by probabilistic method, along with new optimal families, and establish the relationship between optimal $(n,t,w,w-2)$-LPECC codes and optimal $(n+1,t,w,w-2)$-CPECC codes.
