A Framework of Constructing Placement Delivery Arrays for Centralized Coded Caching

In caching system, it is desirable to design a coded scheme with the transmission load $R$ and subpacketization notation="LaTeX">$F$ as small possible, in order improve efficiency of peak traffic times decrease implementation complexity. Yan et al. reformulated centralized designing corresponding notation="LaTeX">$F\times K$ array called placement delivery (PDA), where notation="LaTeX">$K$ number users. Motivated by several constructions PDAs, we introduce framework for constructing each row indexed vector some matrix index column’s labelled an element direct product set. Using this framework, new obtained, which can be regarded generalization previously known schemes. When equal notation="LaTeX">${\binom{m}{ t}}q^{t}$ positive integers notation="LaTeX">$m$ , notation="LaTeX">$t$ notation="LaTeX">$t < m$ notation="LaTeX">$q\geq 2$ show that must orthogonal if all users have same memory size. Furthermore, covering gain t}}$ maximal under our framework. Consequently lower bounds on schemes are derived Finally, using arrays matrix, obtain two more explicit classes significantly advantages while or close constructed Shangguan