Block cipher information leakage using same key
The reason for the 'birthday bound' in block ciphers are collisions that may occur after an expected $2^{n/2}$ blocks (or lack there-of); cases where the inputs to the block cipher is exactly the same (and hence the output is as well).

How might someone, with a large amount of ciphertext, find such collisions in the mode in question?  Having found such a collision, how might they use it to deduce information about the plaintext?