MDS codes on the erasure-erasure wiretap channel

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.