  This paper considers the problem of perfectly secure communication on a
modified version of Wyner's wiretap channel II where both the main and
wiretapper's channels have some erasures. A secret message is to be encoded
into $n$ channel symbols and transmitted. The main channel is such that the
legitimate receiver receives the transmitted codeword with exactly $n - \nu$
erasures, where the positions of the erasures are random. Additionally, an
eavesdropper (wire-tapper) is able to observe the transmitted codeword with $n
- \mu$ erasures in a similar fashion. This paper studies the maximum achievable
information rate with perfect secrecy on this channel and gives a coding scheme
using nested codes that achieves the secrecy capacity.
