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Jean-marie Gorce - One of the best experts on this subject based on the ideXlab platform.
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Approximate Capacity Region of the Two-User Gaussian Interference Channel With Noisy Channel-Output Feedback
IEEE Transactions on Information Theory, 2018Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:In this paper, the capacity region of the linear deterministic interference Channel with noisy Channel-Output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting, block-Markov superposition coding, and backward decoding. The proof of the converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits.
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Decentralized Interference Channels with Noisy Output Feedback
2017Co-Authors: Victor Quintero, Jean-marie Gorce, Samir Perlaza, H Vincent PoorAbstract:In this research report, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference Channel with noisy Channel-Output feedback is characterized for all $\eta > 0$ arbitrarily small. It also characterizes the $\eta$-Nash achievable region of the two-user Gaussian interference with noisy Channel Output feedback for all $\eta > 1$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per Channel use. Existing results such as the $\eta$-NE region of the linear deterministic interference Channel and the Gaussian interference Channel without feedback and with perfect Output feedback are obtained as particular cases of the result presented in this research report.
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Approximate capacity of the Gaussian interference Channel with noisy Channel-Output feedback
2016Co-Authors: Victor Quintero, Inaki Esnaola, Samir Perlaza, Jean-marie GorceAbstract:—In this paper, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-Output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per Channel use.
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When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?
2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:The 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., $\overrightarrow{n}_{11}$ and $\overrightarrow{n}_{22}$; between each transmitter and its corresponding non-intended receiver i.e., $n_{12}$ and $n_{21}$; and between each receiver and its corresponding transmitter, i.e., $\overleftarrow{n}_{11}$ and $\overleftarrow{n}_{22}$. An LD-IC without feedback corresponds to the case in which $\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0$ and the capacity region is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$. In the case in which feedback is available at both transmitters, $\overleftarrow{n}_{11} > 0$ and $\overleftarrow{n}_{22} > 0$, the capacity is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22})$. This paper presents the exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) for observing an improvement in the capacity region $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})$) with respect to $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$, for any $4$-tuple $(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}) \in \mathbb{N}^4$. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair $1$ (resp. $2$), denoted by $\overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22}^{\star}$) for which any $\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}$) enlarges the capacity region, i.e., $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)\subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21} , 0, \overleftarrow{n}_{22})$). The exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) to observe an improvement on a single rate or the sum-rate capacity, for any $4$-tuple $(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21})$ $\in \mathbb{N}^4$ are also presented in this paper.
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CrownCom - When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?
Lecture Notes of the Institute for Computer Sciences Social Informatics and Telecommunications Engineering, 2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:The 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., $\overrightarrow{n}_{11}$ and $\overrightarrow{n}_{22}$; between each transmitter and its corresponding non-intended receiver i.e., $n_{12}$ and $n_{21}$; and between each receiver and its corresponding transmitter, i.e., $\overleftarrow{n}_{11}$ and $\overleftarrow{n}_{22}$. An LD-IC without feedback corresponds to the case in which $\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0$ and the capacity region is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$. In the case in which feedback is available at both transmitters, $\overleftarrow{n}_{11} > 0$ and $\overleftarrow{n}_{22} > 0$, the capacity is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22})$. This technical report presents the exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) for observing an improvement in the capacity region $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})$) with respect to $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$, for any $4$-tuple $(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}) \in \mathbb{N}^4$. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair $1$ (resp. $2$), denoted by $\overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22}^{\star}$) for which any $\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}$) enlarges the capacity region, i.e., $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}$, $0$ , $0) \subset C(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}$, $0$, $\overleftarrow{n}_{22})$). The exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) to observe an improvement on a single rate or the sum-rate capacity, for any $4$-tuple $(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21})$ $\in \mathbb{N}^4$ are also presented in this technical report.
Victor Quintero - One of the best experts on this subject based on the ideXlab platform.
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Approximate Capacity Region of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback
IEEE Transactions on Information Theory, 2018Co-Authors: Victor QuinteroAbstract:In this paper, the capacity region of the linear deterministic interference Channel with noisy Channel-Output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting; block-Markov superposition coding; and backward decoding. The proof of converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (GIC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits.
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Approximate Capacity Region of the Two-User Gaussian Interference Channel With Noisy Channel-Output Feedback
IEEE Transactions on Information Theory, 2018Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:In this paper, the capacity region of the linear deterministic interference Channel with noisy Channel-Output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting, block-Markov superposition coding, and backward decoding. The proof of the converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits.
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Decentralized Interference Channels with Noisy Output Feedback
2017Co-Authors: Victor Quintero, Jean-marie Gorce, Samir Perlaza, H Vincent PoorAbstract:In this research report, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference Channel with noisy Channel-Output feedback is characterized for all $\eta > 0$ arbitrarily small. It also characterizes the $\eta$-Nash achievable region of the two-user Gaussian interference with noisy Channel Output feedback for all $\eta > 1$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per Channel use. Existing results such as the $\eta$-NE region of the linear deterministic interference Channel and the Gaussian interference Channel without feedback and with perfect Output feedback are obtained as particular cases of the result presented in this research report.
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Approximate capacity of the Gaussian interference Channel with noisy Channel-Output feedback
2016Co-Authors: Victor Quintero, Inaki Esnaola, Samir Perlaza, Jean-marie GorceAbstract:—In this paper, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-Output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per Channel use.
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When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?
2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:The 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., $\overrightarrow{n}_{11}$ and $\overrightarrow{n}_{22}$; between each transmitter and its corresponding non-intended receiver i.e., $n_{12}$ and $n_{21}$; and between each receiver and its corresponding transmitter, i.e., $\overleftarrow{n}_{11}$ and $\overleftarrow{n}_{22}$. An LD-IC without feedback corresponds to the case in which $\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0$ and the capacity region is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$. In the case in which feedback is available at both transmitters, $\overleftarrow{n}_{11} > 0$ and $\overleftarrow{n}_{22} > 0$, the capacity is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22})$. This paper presents the exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) for observing an improvement in the capacity region $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})$) with respect to $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$, for any $4$-tuple $(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}) \in \mathbb{N}^4$. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair $1$ (resp. $2$), denoted by $\overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22}^{\star}$) for which any $\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}$) enlarges the capacity region, i.e., $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)\subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21} , 0, \overleftarrow{n}_{22})$). The exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) to observe an improvement on a single rate or the sum-rate capacity, for any $4$-tuple $(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21})$ $\in \mathbb{N}^4$ are also presented in this paper.
Ashutosh Sabharwal - One of the best experts on this subject based on the ideXlab platform.
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Capacity of All Nine Models of Channel Output Feedback for the Two-user Interference Channel
IEEE Transactions on Information Theory, 2013Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In this paper, we study the impact of different Channel Output feedback architectures on the capacity of the two-user interference Channel. For a two-user interference Channel, a feedback link can exist between receivers and transmitters in 9 canonical architectures (see Fig. 2), ranging from only one feedback link to four feedback links. We derive the exact capacity region for the symmetric deterministic interference Channel and the constant-gap capacity region for the symmetric Gaussian interference Channel for all of the 9 architectures. We show that for a linear deterministic symmetric interference Channel, in the weak interference regime, all models of feedback, except the one, which has only one of the receivers feeding back to its own transmitter, have the identical capacity region. When only one of the receivers feeds back to its own transmitter, the capacity region is a strict subset of the capacity region of the rest of the feedback models in the weak interference regime. However, the sum-capacity of all feedback models is identical in the weak interference regime. Moreover, in the strong interference regime all models of feedback with at least one of the receivers feeding back to its own transmitter have the identical sum-capacity. For the Gaussian interference Channel, the results of the linear deterministic model follow, where capacity is replaced with approximate capacity.
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ISIT - Sum capacity of general deterministic interference Channel with Channel Output feedback
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In a two-user interference Channel, there are four possible feedback paths - two from each receiver to the transmitters. This leads to 16 possible models of feedback. In this paper, we derive the sum capacity of two user deterministic interference Channel for all sixteen cases. We find that whenever any of the direct link feedback from a receiver to its own transmitter is present, the sum-capacity is the same as when all four feedback links are present. Further when no direct link feedback is present, the sum capacity with one cross-link feedback and two cross-links of feedback is the same. This sum-capacity is the same as the sum-capacity when there is no feedback except in the regime of interference in which both interfering links are weaker than both the direct-links in which case the sum-capacity is the same as sum-capacity of the feedback model with all four feedback links.
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On Channel Output feedback in deterministic interference Channels
2009 IEEE Information Theory Workshop, 2009Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In this paper, we study the effect of Channel Output feedback on the sum capacity in a two-user symmetric deterministic interference Channel. We find that having a single feedback link from one of the receivers to its own transmitter results in the same sum capacity as having a total of 4 feedback links from both the receivers to both the transmitters. Hence, from the sum capacity point of view, the three additional feedback links are not helpful. We also consider a half-duplex feedback model, where the forward and the feedback resources are symmetric and time-shared. Surprisingly, we find that there is no gain in sum-capacity with feedback in a half-duplex feedback model, when interference links have more capacity than direct links.
Samir M. Perlaza - One of the best experts on this subject based on the ideXlab platform.
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Approximate Capacity Region of the Two-User Gaussian Interference Channel With Noisy Channel-Output Feedback
IEEE Transactions on Information Theory, 2018Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:In this paper, the capacity region of the linear deterministic interference Channel with noisy Channel-Output feedback (LD-IC-NF) is fully characterized. The proof of achievability is based on random coding arguments and rate splitting, block-Markov superposition coding, and backward decoding. The proof of the converse reuses some of the existing outer bounds and includes new ones obtained using genie-aided models. Following the insight gained from the analysis of the LD-IC-NF, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NF) are presented. Finally, the achievability region and the converse region are proven to approximate the capacity region of the G-IC-NF to within 4.4 bits.
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When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?
2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:The 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., $\overrightarrow{n}_{11}$ and $\overrightarrow{n}_{22}$; between each transmitter and its corresponding non-intended receiver i.e., $n_{12}$ and $n_{21}$; and between each receiver and its corresponding transmitter, i.e., $\overleftarrow{n}_{11}$ and $\overleftarrow{n}_{22}$. An LD-IC without feedback corresponds to the case in which $\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0$ and the capacity region is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$. In the case in which feedback is available at both transmitters, $\overleftarrow{n}_{11} > 0$ and $\overleftarrow{n}_{22} > 0$, the capacity is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22})$. This paper presents the exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) for observing an improvement in the capacity region $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})$) with respect to $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$, for any $4$-tuple $(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}) \in \mathbb{N}^4$. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair $1$ (resp. $2$), denoted by $\overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22}^{\star}$) for which any $\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}$) enlarges the capacity region, i.e., $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)\subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21} , 0, \overleftarrow{n}_{22})$). The exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) to observe an improvement on a single rate or the sum-rate capacity, for any $4$-tuple $(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21})$ $\in \mathbb{N}^4$ are also presented in this paper.
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CrownCom - When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?
Lecture Notes of the Institute for Computer Sciences Social Informatics and Telecommunications Engineering, 2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:The 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., $\overrightarrow{n}_{11}$ and $\overrightarrow{n}_{22}$; between each transmitter and its corresponding non-intended receiver i.e., $n_{12}$ and $n_{21}$; and between each receiver and its corresponding transmitter, i.e., $\overleftarrow{n}_{11}$ and $\overleftarrow{n}_{22}$. An LD-IC without feedback corresponds to the case in which $\overleftarrow{n}_{11} = \overleftarrow{n}_{22} = 0$ and the capacity region is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$. In the case in which feedback is available at both transmitters, $\overleftarrow{n}_{11} > 0$ and $\overleftarrow{n}_{22} > 0$, the capacity is denoted by $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , \overleftarrow{n}_{22})$. This technical report presents the exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) for observing an improvement in the capacity region $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , \overleftarrow{n}_{22})$) with respect to $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0)$, for any $4$-tuple $(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}) \in \mathbb{N}^4$. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair $1$ (resp. $2$), denoted by $\overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22}^{\star}$) for which any $\overleftarrow{n}_{11} > \overleftarrow{n}_{11}^{\star}$ (resp. $\overleftarrow{n}_{22} > \overleftarrow{n}_{22}^{\star}$) enlarges the capacity region, i.e., $C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, 0 , 0) \subset C(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21}, \overleftarrow{n}_{11} , 0)$ (resp. $C(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}$, $0$ , $0) \subset C(\overrightarrow{n}_{11}$, $\overrightarrow{n}_{22}$, $n_{12}$, $n_{21}$, $0$, $\overleftarrow{n}_{22})$). The exact conditions on $\overleftarrow{n}_{11}$ (resp. $\overleftarrow{n}_{22}$) to observe an improvement on a single rate or the sum-rate capacity, for any $4$-tuple $(\overrightarrow{n}_{11}, \overrightarrow{n}_{22}, n_{12}, n_{21})$ $\in \mathbb{N}^4$ are also presented in this technical report.
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Approximate Capacity of the Two-User Gaussian Interference Channel with Noisy Channel-Output Feedback
2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:In this research report, an achievability region and a converse region for the two-user Gaussian interference Channel with noisy Channel-Output feedback (G-IC-NOF) are presented. The achievability region is obtained using a random coding argument and three well-known techniques: rate splitting, superposition coding and backward decoding. The converse region is obtained using some of the existing perfect-Output feedback outer-bounds as well as a set of new outer-bounds that are obtained by using genie-aided models of the original G-IC-NOF. Finally, it is shown that the achievability region and the converse region approximate the capacity region of the G-IC-NOF to within a constant gap in bits per Channel use.
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When Does Channel-Output Feedback Enlarge the Capacity Region of the Interference Channel?
2016Co-Authors: Victor Quintero, Samir M. Perlaza, Inaki Esnaola, Jean-marie GorceAbstract:In this research report, the benefits of Channel-Output feedback in the Gaussian interference Channel (G-IC) are studied under the effect of additive Gaussian noise. Using a linear deterministic (LD) model, the signal to noise ratios (SNRs) in the feedback links beyond which feedback plays a significant role in terms of increasing the individual rates or the sum-rate are approximated. The relevance of this work lies on the fact that it identifies the feedback SNRs for which in any G-IC one of the following statements is true: (a) Feedback does not enlarge the capacity region; (b) Feedback enlarges the capacity region and the sum-rate is higher than the largest sum-rate without feedback; and (c) Feedback enlarges the capacity region but no significant improvement is observed in the sum-rate.
Achaleshwar Sahai - One of the best experts on this subject based on the ideXlab platform.
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Capacity of All Nine Models of Channel Output Feedback for the Two-user Interference Channel
IEEE Transactions on Information Theory, 2013Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In this paper, we study the impact of different Channel Output feedback architectures on the capacity of the two-user interference Channel. For a two-user interference Channel, a feedback link can exist between receivers and transmitters in 9 canonical architectures (see Fig. 2), ranging from only one feedback link to four feedback links. We derive the exact capacity region for the symmetric deterministic interference Channel and the constant-gap capacity region for the symmetric Gaussian interference Channel for all of the 9 architectures. We show that for a linear deterministic symmetric interference Channel, in the weak interference regime, all models of feedback, except the one, which has only one of the receivers feeding back to its own transmitter, have the identical capacity region. When only one of the receivers feeds back to its own transmitter, the capacity region is a strict subset of the capacity region of the rest of the feedback models in the weak interference regime. However, the sum-capacity of all feedback models is identical in the weak interference regime. Moreover, in the strong interference regime all models of feedback with at least one of the receivers feeding back to its own transmitter have the identical sum-capacity. For the Gaussian interference Channel, the results of the linear deterministic model follow, where capacity is replaced with approximate capacity.
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ISIT - Sum capacity of general deterministic interference Channel with Channel Output feedback
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In a two-user interference Channel, there are four possible feedback paths - two from each receiver to the transmitters. This leads to 16 possible models of feedback. In this paper, we derive the sum capacity of two user deterministic interference Channel for all sixteen cases. We find that whenever any of the direct link feedback from a receiver to its own transmitter is present, the sum-capacity is the same as when all four feedback links are present. Further when no direct link feedback is present, the sum capacity with one cross-link feedback and two cross-links of feedback is the same. This sum-capacity is the same as the sum-capacity when there is no feedback except in the regime of interference in which both interfering links are weaker than both the direct-links in which case the sum-capacity is the same as sum-capacity of the feedback model with all four feedback links.
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On Channel Output feedback in deterministic interference Channels
2009 IEEE Information Theory Workshop, 2009Co-Authors: Achaleshwar Sahai, Melda Yüksel, Vaneet Aggarwal, Ashutosh SabharwalAbstract:In this paper, we study the effect of Channel Output feedback on the sum capacity in a two-user symmetric deterministic interference Channel. We find that having a single feedback link from one of the receivers to its own transmitter results in the same sum capacity as having a total of 4 feedback links from both the receivers to both the transmitters. Hence, from the sum capacity point of view, the three additional feedback links are not helpful. We also consider a half-duplex feedback model, where the forward and the feedback resources are symmetric and time-shared. Surprisingly, we find that there is no gain in sum-capacity with feedback in a half-duplex feedback model, when interference links have more capacity than direct links.