2024/02/11 by Rashid Ummer N. T., T., Rashid Ummer N., B. Sundar Rajan +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2402.07188
openalex publication_date 2024/02/11 · openalex created_date 2024/02/14 · openalex updated_date 2026/07/28
Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) achieves an optimal transmission rate R under uncoded placement but requires a subpacketization level F which increases exponentially with the number of users K where the number of files N ≥ K. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan et al. in \citeYCT. This paper proposes two novel classes of PDA constructions from combinatorial t-designs that achieve an improved transmission rate for a given low subpacketization level, cache size and number of users compared to existing coded caching schemes from t-designs. A (K, F, Z, S) PDA composed of a specific symbol ⋆ and S non-negative integers corresponds to a coded caching scheme with subpacketization level F, K users each caching Z packets and the demands of all the users are met with a rate R=(S)/(F). For a given K, F and Z, a lower bound on S such that a (K, F, Z, S) PDA exists is given by Cheng et al. in \citeMJXQ and by Wei in \citeWei . Our first class of proposed PDA achieves the lower bound on S. The second class of PDA also achieves the lower bound in some cases. From these two classes of PDAs, we then construct hierarchical placement delivery arrays (HPDA), proposed by Kong et al. in \citeKYWM, which characterizes a hierarchical two-layer coded caching system. These constructions give low subpacketization level schemes.