Multilevel diversity coding with secrecy constraints

We consider the problem of communicating multiple sources to a receiver amidst an eavesdropper. The source encoder encodes the sources and sends it through the available L channels to the receiver. The eavesdropper has access to a subset of m channels (m < L). There are totally L - m sources to be communicated to the receiver with the stipulation that the receiver needs to be able to reconstruct sources {1, 2 ... k}, by accessing any subset of (m + k) channels (1 les k les L - m). We obtain the coding rate region for the case when L = 3, m = 1 and show that separate and secure encoding of sources is optimal for this problem. For the case of arbitrary m, L we derive a lower bound on the sum rate and the result implies a separation scheme to achieve this lower bound.