4 research outputs found
Optimal Placement Delivery Arrays from -Designs with Application to Hierarchical Coded Caching
Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN)
achieves an optimal transmission rate under uncoded placement but requires
a subpacketization level which increases exponentially with the number of
users where the number of files . Placement delivery array (PDA)
was proposed as a tool to design coded caching schemes with reduced
subpacketization level by Yan \textit{et al.} in \cite{YCT}. This paper
proposes two novel classes of PDA constructions from combinatorial -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 -designs. A PDA composed of a specific symbol
and non-negative integers corresponds to a coded caching scheme
with subpacketization level , users each caching packets and the
demands of all the users are met with a rate . For a given ,
and , a lower bound on such that a PDA exists is
given by Cheng \textit{et al.} in \cite{MJXQ} and by Wei in \cite{Wei} . Our
first class of proposed PDA achieves the lower bound on . 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 \textit{et al.} in \cite{KYWM}, which characterizes a hierarchical
two-layer coded caching system. These constructions give low subpacketization
level schemes.Comment: Title has been changed. Some changes have been incorporated in the
results. 11 pages, 5 figures and 3 table