  We write explicitly a general protocol for faithful teleportation of a
d-state particle (qudit) via a partially entangled pair of (pure) $n$-state
particles. The classical communication cost (CCC) of the protocol is
$\log_{2}(nd)$ bits, and it is implemented by a {\em projective} measurement
performed by Alice, and a unitary operator performed by Bob (after receiving
from Alice the measurement result). We prove the optimality of our protocol by
a comparison with the concentrate and teleport strategy. We also show that if
$d>n/2$ or if there is no residual entanglement left after the faithful
teleportation, the CCC of {\em any} protocol is at least $\log_{2}(nd)$ bits.
Furthermore, we find a lower bound on the CCC in the process transforming one
bipartite state to another by means of local operation and classical
communication (LOCC).
