“…Proof: The proof follows the same lines as that of Theorem 1 except that in this case, since V 1 , V 2 are independent of S 1 , S 2 , the encoding scheme does not include binning and during the codebook generation process, instead of generating 2 n R k +R k , k = 1, 2, n-sequences v n k , we only generate 2 nR k such sequences. Therefore, by negligibly altering the codebook generated we can easily derive the expressions in (17). In fact, if the senders want to send (m 1b , m 2b ) to the receiver, upon choosing the helping index m 0b , they find the suitable u n , v n 1 and v n 2 sequences directly and then send x n 1 and x n 2 where…”