Improved Coded Caching from Two New Classes of PDAs from t-Designs
Rashid Ummer N. T., Balaji Sundar Rajan · 2024
Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) achieves 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$N\geq K$. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan et al. in [4]. This paper proposes two novel classes of PDA constructions from combinatorial t-designs which achieve 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$\star$and$S$nonnegative 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$R=\frac{S}{F}$. 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 [16]. The first class of proposed PDA achieves this lower bound on S. The second class of PDA also achieves this lower bound in some cases.