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## Feedback Can Double the Prelog of Some Memoryless Gaussian Networks

Citations: | 3 - 2 self |

### Citations

12375 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...: E[X2]≤P {I(X ;Y1) + I(X ;Y2)} = 1 2 log ( 1 + P σ21 ) + 1 2 log ( 1 + P σ22 ) , (65) where the equality follows because a Gaussian law maximizes the differential entropy under a variance constraint =-=[22]-=-. When ρz ∈ (−1, 1) and ρz /∈ { σ2 σ1 , σ1σ2 } , the achievability follows from Corollary 10 and the converse by applying the cutset bound with a single cut between the transmitter and both receivers:... |

571 | Broadcast channels
- Cover
- 1972
(Show Context)
Citation Context ...apacity of our setup CBC,Σ is unknown except for the physically degraded case where ρz ∈ { σ1 σ2 , σ2 σ1 } . (13) In this case the capacity region is not increased with feedback [19], and thus, [20], =-=[21]-=- CBC,Σ(P, σ 2 1 , σ 2 2 , ρz) = 1 2 log ( 1 + P min{σ21 , σ22} ) . (14) The AWGN BC with feedback is in particular physically degraded if ρz = 1 and σ21 = σ22 , in which case both receivers observe ex... |

478 | A new achievable rate region for the interference channel - Han, Kobayashi - 1981 |

238 |
The capacity of the Gaussian interference channel under strong interference
- Sato
- 1981
(Show Context)
Citation Context ... of the AWGN MAC from both transmitters to one of the two receivers, and its prelog is 1 [26]. To prove the converse to (35) when ρz ∈ (−1, 1) we use a genie-argument and a generalized Sato-MAC bound =-=[27]-=-, similar to the upper bounds in [28, Section V-B], [29], [30], [31]. Our proof consists of the following three steps. In the first step we let a genie prior to transmission reveal the symbols Un = Zn... |

136 |
A simple converse for broadcast channels with additive white Gaussian noise
- Bergmans
- 1974
(Show Context)
Citation Context ... sum-capacity of our setup CBC,Σ is unknown except for the physically degraded case where ρz ∈ { σ1 σ2 , σ2 σ1 } . (13) In this case the capacity region is not increased with feedback [19], and thus, =-=[20]-=-, [21] CBC,Σ(P, σ 2 1 , σ 2 2 , ρz) = 1 2 log ( 1 + P min{σ21 , σ22} ) . (14) The AWGN BC with feedback is in particular physically degraded if ρz = 1 and σ21 = σ22 , in which case both receivers obse... |

125 |
The capacity of the white gaussian multiple access channel with feedback
- Ozarow
- 1984
(Show Context)
Citation Context ...her receiver’s outputs. Consequently, the feedback capacity of our AWGN IC coincides with the feedback capacity of the AWGN MAC from both transmitters to one of the two receivers, and its prelog is 1 =-=[26]-=-. To prove the converse to (35) when ρz ∈ (−1, 1) we use a genie-argument and a generalized Sato-MAC bound [27], similar to the upper bounds in [28, Section V-B], [29], [30], [31]. Our proof consists ... |

94 |
Outer bounds on the capacity of Gaussian interference channels
- Kramer
- 2004
(Show Context)
Citation Context ...o receivers, and its prelog is 1 [26]. To prove the converse to (35) when ρz ∈ (−1, 1) we use a genie-argument and a generalized Sato-MAC bound [27], similar to the upper bounds in [28, Section V-B], =-=[29]-=-, [30], [31]. Our proof consists of the following three steps. In the first step we let a genie prior to transmission reveal the symbols Un = Zn2 − a2,2 a1,2 Zn1 to Receiver 1. This obviously can only... |

81 |
Gaussian feedback capacity
- Cover, Pombra
- 1989
(Show Context)
Citation Context ... (with or without feedback) cannot exceed the number of transmit (or receive) antennas [1]. To demonstrate these gains we propose and analyze a novel feedback coding scheme, similar to the schemes in =-=[4]-=-, [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], [9] if the scheme’s parameter are chosen carefully, see [10], [11].) Our proposed cod... |

72 |
Feedback strategies for white Gaussian interference networks
- Kramer
- 2002
(Show Context)
Citation Context ...interference channel is symmetric, the prelog 2 result can also be shown using a slight generalization (to account for the correlation between the noise sequences) of Kramer’s memoryless LMMSE-scheme =-=[14]-=-.) Previously, a prelog of 2 was known to be achievable for the two-user scalar AWGN IC only when the two transmitters (or the two receivers) could fully cooperate [15] in the sense that both transmit... |

70 |
An achievable region and outer bound for the gaussian broadcast channel with feedback
- Ozarow, Leung-Yan-Cheong
- 1984
(Show Context)
Citation Context ... we propose and analyze a novel feedback coding scheme, similar to the schemes in [4], [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], =-=[9]-=- if the scheme’s parameter are chosen carefully, see [10], [11].) Our proposed coding scheme also allows us to determine the high-SNR asymptotics of the sum-capacity of the tworeceiver AWGN BC with no... |

67 | Feedback capacity of the Gaussian interference channel to within 2 bits
- Suh, Tse
- 2011
(Show Context)
Citation Context ... BC and for the symmetric two-user AWGN IC where the individual noise sequences corrupting the outputs at the two receivers are perfectly anticorrelated. The same conclusion was later also reached in =-=[3]-=-, [16] (also based on the scheme proposed in [17]) for the twouser AWGN IC when the noise sequences are independent. Multiplicative gains for the AWGN IC with independent noises at moderate SNR were a... |

47 | Interference channel with generalized feedback (a.k.a. with source cooperation): part I: achievable region
- Yang, Tuninetti
- 2011
(Show Context)
Citation Context ... the individual noise sequences corrupting the outputs at the two receivers are perfectly anticorrelated. The same conclusion was later also reached in [3], [16] (also based on the scheme proposed in =-=[17]-=-) for the twouser AWGN IC when the noise sequences are independent. Multiplicative gains for the AWGN IC with independent noises at moderate SNR were already reported in [14, Section VI-B]. We conclud... |

34 |
The feedback capacity of degraded broadcast channels
- Gamal
- 1978
(Show Context)
Citation Context ...+ P ) . (12) The sum-capacity of our setup CBC,Σ is unknown except for the physically degraded case where ρz ∈ { σ1 σ2 , σ2 σ1 } . (13) In this case the capacity region is not increased with feedback =-=[19]-=-, and thus, [20], [21] CBC,Σ(P, σ 2 1 , σ 2 2 , ρz) = 1 2 log ( 1 + P min{σ21 , σ22} ) . (14) The AWGN BC with feedback is in particular physically degraded if ρz = 1 and σ21 = σ22 , in which case bot... |

27 |
Partial feedback for two-way and broadcast channels
- Dueck
- 1980
(Show Context)
Citation Context ...his case, our scheme achieves the rate pair R1 = 12 log + ( P σ2 1 ) , R2 = 1 2 log + ( P σ2 2 ) (see Corollary 11). The special case |ρz | = 1 illustrates very nicely that the intuition put forth in =-=[23]-=-, [9], [24], [25] applies also to our scheme: feedback is helpful for a memoryless BC because it allows the transmitter to identify and transmit information that at the same time is useful for both re... |

24 | Interference channels with ratelimited feedback
- Vahid, Suh, et al.
- 2012
(Show Context)
Citation Context ...result shows that limited cooperation through feedback can be sufficient. For the two-user AWGN IC we do not consider noisy feedback. Rate-limited feedback for this setup has recently been studied in =-=[18]-=-. The fact that feedback can increase the capacity of memoryless networks without bounds was first reported by the authors in [2] for the two-user AWGN BC and for the symmetric two-user AWGN IC where ... |

17 | LQG control approach to Gaussian broadcast channels with feedback,” submitted to the
- Ardestanizadeh, Minero, et al.
- 2011
(Show Context)
Citation Context ...lows us to prove that if the AWGN sequences corrupting the K received signals are all different but have covariance matrix of rank 1, then a prelog of K is achievable. For a related recent result see =-=[12]-=-. A naturally ensuing question is whether these gains in capacity can also be attained when the feedback is noisy. In this paper we concentrate on how feedback noise affects the reported gains in the ... |

15 | On the capacity of the discrete memoryless broadcast channel with feedback
- Shayevitz, Wigger
- 2013
(Show Context)
Citation Context ...eme achieves the rate pair R1 = 12 log + ( P σ2 1 ) , R2 = 1 2 log + ( P σ2 2 ) (see Corollary 11). The special case |ρz | = 1 illustrates very nicely that the intuition put forth in [23], [9], [24], =-=[25]-=- applies also to our scheme: feedback is helpful for a memoryless BC because it allows the transmitter to identify and transmit information that at the same time is useful for both receivers, and ther... |

11 | On the Gaussian MAC with imperfect feedback
- Lapidoth, Wigger
- 2010
(Show Context)
Citation Context ...h or without feedback) cannot exceed the number of transmit (or receive) antennas [1]. To demonstrate these gains we propose and analyze a novel feedback coding scheme, similar to the schemes in [4], =-=[5]-=-, and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], [9] if the scheme’s parameter are chosen carefully, see [10], [11].) Our proposed coding s... |

11 | On cognitive interference networks
- Lapidoth, Shamai
- 2007
(Show Context)
Citation Context ...ivers, and its prelog is 1 [26]. To prove the converse to (35) when ρz ∈ (−1, 1) we use a genie-argument and a generalized Sato-MAC bound [27], similar to the upper bounds in [28, Section V-B], [29], =-=[30]-=-, [31]. Our proof consists of the following three steps. In the first step we let a genie prior to transmission reveal the symbols Un = Zn2 − a2,2 a1,2 Zn1 to Receiver 1. This obviously can only incre... |

10 | Coding and capacity for additive white Gaussian noise multi-user channels with feedback
- Ozarow
- 1979
(Show Context)
Citation Context ...gains we propose and analyze a novel feedback coding scheme, similar to the schemes in [4], [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in =-=[8]-=-, [9] if the scheme’s parameter are chosen carefully, see [10], [11].) Our proposed coding scheme also allows us to determine the high-SNR asymptotics of the sum-capacity of the tworeceiver AWGN BC wi... |

8 | Bounds on the error exponent of the AWGN channel with AWGN corrupted feedback
- Kim, Lapidoth, et al.
- 2006
(Show Context)
Citation Context ...equences—the prelog of the two-user AWGN BC setup equals one (as in the absence of feedback). The proof of this result is based on a genie argument inspired by the work of Kim, Lapidoth, and Weissman =-=[13]-=-. The second network we consider is the two-user scalar AWGN IC with noise-free one-sided feedback where each of the two transmitters communicates with a different intended receiver, and each transmit... |

5 | New achievable rates for the Gaussian broadcast channel with feedback
- Gastpar, Lapidoth, et al.
(Show Context)
Citation Context ... See Section IX-B. VI. A SCHEME AND PROOFS FOR THE AWGN BC WITH NOISE-FREE FEEDBACK A. A coding scheme We present a new coding scheme for the K = 2 user Gaussian BC with noise-free feedback, see also =-=[7]-=-. (The scheme is generalized to K ≥ 2 users in Section VIII-A.) Our scheme is similar to the schemes proposed by Cover and Pombra [4] for (non-white) Gaussian point-to-point channels with noise-free f... |

5 | The pre-log of gaussian broadcast with feedback can be two
- Wigger, Gastpar
- 2008
(Show Context)
Citation Context ...similar to the schemes in [4], [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], [9] if the scheme’s parameter are chosen carefully, see =-=[10]-=-, [11].) Our proposed coding scheme also allows us to determine the high-SNR asymptotics of the sum-capacity of the tworeceiver AWGN BC with noise-free feedback and arbitrary noise correlation. The ex... |

4 |
Gaussian broadcast channel with partial feedback
- Lapidoth, Steinberg, et al.
- 2010
(Show Context)
Citation Context ...out feedback) cannot exceed the number of transmit (or receive) antennas [1]. To demonstrate these gains we propose and analyze a novel feedback coding scheme, similar to the schemes in [4], [5], and =-=[6]-=-. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], [9] if the scheme’s parameter are chosen carefully, see [10], [11].) Our proposed coding scheme als... |

4 |
der Meulen, “Een verbetering en veralgemening van het transmissiegebied van Ozarow voor het Gaussische broadcast kanaal met feedback,” in
- Willems, van
- 1981
(Show Context)
Citation Context ... (36) follows from the general Relation (123), and its achievability from Proposition 13 (Section IX-A). ACKNOWLEDGMENT The authors thank Prof. Frans M. J. Willems, TU Eindhoven, for pointing them to =-=[32]-=-, which inspired the investigation leading to this work. They also thank the Associate Editor and the anonymous reviewers for their valuable comments. APPENDIX A PROOF OF LEMMA 1 Let η ∈ Z+. If 1 + ζ ... |

3 | The pre-log of Gaussian broadcast with feedback can be two
- Gastpar, Wigger
(Show Context)
Citation Context ...ck. Rate-limited feedback for this setup has recently been studied in [18]. The fact that feedback can increase the capacity of memoryless networks without bounds was first reported by the authors in =-=[2]-=- for the two-user AWGN BC and for the symmetric two-user AWGN IC where the individual noise sequences corrupting the outputs at the two receivers are perfectly anticorrelated. The same conclusion was ... |

3 | An achievable region for the discrete memoryless broadcast channel with feedback
- Shayevitz, Wigger
- 2010
(Show Context)
Citation Context ...ur scheme achieves the rate pair R1 = 12 log + ( P σ2 1 ) , R2 = 1 2 log + ( P σ2 2 ) (see Corollary 11). The special case |ρz | = 1 illustrates very nicely that the intuition put forth in [23], [9], =-=[24]-=-, [25] applies also to our scheme: feedback is helpful for a memoryless BC because it allows the transmitter to identify and transmit information that at the same time is useful for both receivers, an... |

2 |
The capacity of a channel with Gaussian noise and intersymbol interference
- Algoet, Cioffi
- 1991
(Show Context)
Citation Context ...st to the case where the received signals are corrupted by independent AWGN sequences, a case in which the prelog (with or without feedback) cannot exceed the number of transmit (or receive) antennas =-=[1]-=-. To demonstrate these gains we propose and analyze a novel feedback coding scheme, similar to the schemes in [4], [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the ... |

2 |
The multiplexing gain of MIMO X-channels wiht partial transmit side information
- Devroye, Sharif
- 2007
(Show Context)
Citation Context ...ramer’s memoryless LMMSE-scheme [14].) Previously, a prelog of 2 was known to be achievable for the two-user scalar AWGN IC only when the two transmitters (or the two receivers) could fully cooperate =-=[15]-=- in the sense that both transmitters can compute their channel inputs as a function of both messages. Our result shows that limited cooperation through feedback can be sufficient. For the two-user AWG... |

2 |
A cognitive interference network with clustered decoding
- Lapidoth, Levy, et al.
(Show Context)
Citation Context ... and its prelog is 1 [26]. To prove the converse to (35) when ρz ∈ (−1, 1) we use a genie-argument and a generalized Sato-MAC bound [27], similar to the upper bounds in [28, Section V-B], [29], [30], =-=[31]-=-. Our proof consists of the following three steps. In the first step we let a genie prior to transmission reveal the symbols Un = Zn2 − a2,2 a1,2 Zn1 to Receiver 1. This obviously can only increase th... |

1 |
When feedback doubles the prelog
- Gastpar, Lapidoth, et al.
- 2010
(Show Context)
Citation Context ...r to the schemes in [4], [5], and [6]. (The gains for anti-correlated AWGN sequences are also achieved by the Ozarow-Leung scheme in [8], [9] if the scheme’s parameter are chosen carefully, see [10], =-=[11]-=-.) Our proposed coding scheme also allows us to determine the high-SNR asymptotics of the sum-capacity of the tworeceiver AWGN BC with noise-free feedback and arbitrary noise correlation. The expansio... |