M. 3?12, M 1?23,l (2) = (M 3?12,l?1 , M 1?23,l ), vol.1

. H-private-;-=-m-3?2, M 1?2,l (2) = (M 3?2,l?1 , M 1?2,l ), vol.1

, From these definitions, we can easily deduce that: Pr {E dec (2, l) ? F l ? G l (2, 13)}=Pr {H common (2, l) ? F l ? G l (2, 13)} +Pr H private

, ?Pr {K common (2, l)} + Pr {K private

, where K common (2, l)= ?(m 1?23,l ,m 3?12,l?1 ) = (M 1?23,l , M 3?12,l?1 )

?. 1?23 and ). ,

, K private (2, l)= ?(m 1?2,l ,m 3?2,l?1 ) = (M 1?2,l , M 3?2,l?1 )

?. 1?2 and ). ,

, dp (2, l) are carefully chosen 15 , and for a saving of notation we considered only the indices to be recovered

, Node 2 has to recover two indices from a binning structure as the one in the cooperative Berger-Tung problem described in Appendix B. In Fig. 10, we have a representation of the problem seen at decoder 2, Consider first the recovering of the common information

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