A Low-Latency Strategy for Asymmetric Hierarchical Coded Caching

Coded caching is a technique designed to reduce network traffic load during peak traffic times. While numerous studies have focused on single-layer caching systems, real-world networks typically exhibit hierarchical tree-like structures. We investigate an asymmetric hierarchical coded caching model where a server stores N files and connects to K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> mirrors (K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ≥ 2) and K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> users via an error-free shared link, with each mirror serving K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> users. Each mirror and user is equipped with caches of size M<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and M<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>, respectively. We propose a decentralized coded caching scheme that reduces transmission delay by enabling concurrent transmission between the two layers. For K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> = 2 or 3, we derive closed-form mathematical expressions for the achievable coding delay of our proposed scheme, while for K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> ≥ 4, we employ computational methods to establish the relationship between the achievable coding delay and cache size. Additionally, we develop a novel lower bound for coding delay that is tighter than that obtained through the cut-set bound. Numerical results demonstrate that our proposed scheme outperforms the existing ones.