  In private information delivery (PID) problem, there are $K$ messages stored
across $N$ servers, each capable of storing $M$ messages and a user. Servers
want to convey one of the $K$ messages to the user without revealing the
identity (index) of the message conveyed. The capacity of PID problem is
defined as maximum number of bits of the desired message that can be conveyed
privately, per bit of total communication, to the user. For the restricted case
of replicated systems, where coded messages or splitting one message into
several servers is not allowed, the capacity of PID has been characterized by
Hua Sun in "Private Information Delivery, IEEE Transactions on Information
Theory, December 2020" in terms of $K, N$ and $M.$ In this paper, we study the
problem of PID with coded storage at the servers. For a class of problems
called {\it bi-regular PID} we characterize the capacity for $N=K/M$ and for
$N>K/M$ we provide an achievable scheme. In both the cases the rates achieved
are more than the rates achievable with the replicated systems.
