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    When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?

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    International audienceThe two-user linear deterministic interference channel (LD-IC) with noisy channel-output feedback is fully described by six parameters that correspond to the number of bit-pipes between each transmitter and its corresponding intended receiver, i.e., n11\overrightarrow{n}_{11} and n22\overrightarrow{n}_{22}; between each transmitter and its corresponding non-intended receiver i.e., n12n_{12} and n21n_{21}; and between each receiver and its corresponding transmitter, i.e., n11\overleftarrow{n}_{11} and n22\overleftarrow{n}_{22}. An LD-IC without feedback corresponds to the case in which n11=n22=0\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0 and the capacity region is denoted by C(n11,n22,n12,n21,0,0)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0). In the case in which feedback is available at both transmitters, n11>0\overleftarrow{n}_{11} > 0 and n22>0\overleftarrow{n}_{22} > 0, the capacity is denoted by C(n11,n22,n12,n21,n11,n22)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22}).This paper presents the exact conditions on n11\overleftarrow{n}_{11} (resp. n22\overleftarrow{n}_{22}) for observing an improvement in the capacity region C(n11,n22,n12,n21,n11,0)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0) (resp. C(n11,n22,n12,n21,0,n22)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})) with respect to C(n11,n22,n12,n21,0,0)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0), for any 44-tuple (n11(\overrightarrow{n}_{11}, n22\overrightarrow{n}_{22}, n12n_{12}, n21)N4n_{21}) \in \mathbb{N}^4.Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair 11 (resp. 22), denoted by n11\overleftarrow{n}_{11}^{\star} (resp. n22\overleftarrow{n}_{22}^{\star}) for which any n11>n11\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star} (resp. n22>n22\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}) enlarges the capacity region, i.e., C(n11,n22,n12,n21,0,0)C(n11,n22,n12,n21,n11,0)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0) (resp. C(n11,n22,n12,n21,0,0)C(n11,n22,n12,n21,0,n22)C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)\subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21} , 0, \overleftarrow{n}_{22})).The exact conditions on n11\overleftarrow{n}_{11} (resp. n22\overleftarrow{n}_{22}) to observe an improvement on a single rate or the sum-rate capacity, for any 44-tuple (n11,n22,n12,n21)(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}) N4\in \mathbb{N}^4 are also presented in this paper
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