Third-party cyclic code reconstruction over binary erasure channel (Q2098078)

Summary: We consider a setup where Alice is transmitting channel coded messages to Bob and intruder Willie is snooping over this communication. Willie does not know the channel code that Alice is using and wishes to identify it in order to decode the intercepted messages. This problem is termed as \textit{blind reconstruction of channel codes} and has possible applications in cognitive radios and military. In this work, we consider the situation when Willie knows that Alice's channel code belongs to the family of binary cyclic codes and the underlying communication channel is the binary erasure channel. We present an algorithm to identify the parameters of the unknown channel code corresponding to the given data. The key step in our algorithm consists of distinguishing between the two situations when all of the assumed parameters are correct and when either of the parameter is incorrect. As part of analysis, we present a lower bound on probability of correctly distinguishing between these two situations.