  Bound entangled (BE) states are strange in nature: non-zero amount of free
entanglement is required to create them but no free entanglement can be
distilled from them under local operations and classical communication (LOCC).
Even though usefulness of such states has been shown in several information
processing tasks, there exists no simple method to characterize them for an
arbitrary composite quantum system. Here we present a $(d-3)/2$-parameter
family of BE states each with positive partial transpose (PPT). This family of
PPT-BE states is introduced by constructing an unextendible product basis (UPB)
in $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d$ odd and $d\ge 5$. The range of
each such PPT-BE state is contained in a $2(d-1)$ dimensional entangled
subspace whereas the associated UPB-subspace is of dimension $(d-1)^2+1$. We
further show that each of these PPT-BE states can be written as a convex
combination of $(d-1)/2$ number of rank-4 PPT-BE states. Moreover, we prove
that these rank-4 PPT-BE states are extreme points of the convex compact set
$\mathcal{P}$ of all PPT states in $\mathbb{C}^d\otimes\mathbb{C}^d$, namely
the {\it Peres} set. An interesting geometric implication of our result is that
the convex hull of these rank-4 PPT-BE extreme points -- the $(d-3)/2$-simplex
-- is sitting on the boundary between the set $\mathcal{P}$ and the set of
non-PPT states. We also discuss consequences of our construction in the context
of quantum state discrimination by LOCC.
