Abstract-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 − ν erasures, where the positions of the erasures are random. Additionally, an eavesdropper (wire-tapper) is able to observe the transmitted codeword with n − µ 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.
A modified version of the wiretap channel II is considered in REF , where the number of erasures at the eavesdropper is fixed.
MDS codes on the erasure-erasure wiretap channel
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Mathematics Computer Science