### Citations

478 |
A new achievable rate region for the interference channel
- Han, Kobayashi
- 1981
(Show Context)
Citation Context ... at each receiver due to this channel model’s linearity, in which case the physical channel model reduces to two oneway IC in opposite directions. We may thus apply the wellknown Han–Kobayashi scheme =-=[33]-=- in each direction, ignoring the ability of the nodes to adapt, achieving the expression in (IC→) and (IC←). Now we prove the converse. Single-rates follow as in (6), and using Lemma 8 (where we use p... |

447 | Gaussian interference channel capacity to within one bit
- Etkin, Tse, et al.
- 2008
(Show Context)
Citation Context ...not very strong interference, non-adaptive schemes perform to within 1 bit per user per direction of the fully adaptive capacity region, and c) the particular non-adaptive Han and Kobayashi scheme of =-=[9]-=- employed in each direction, achieves to within a constant gap (2 bits per user per direction maximally) of fully or partially adaptive outer bounds in all other regimes. We provide examples of non-sy... |

390 |
Network Information theory
- Gamal, Kim
- 2011
(Show Context)
Citation Context ...el considered is the two-way linear deterministic IC in which there are 4 messages and 4 terminals forming ICs in the → and ← directions. The capacity region of the one-way modulo 2 adder IC is known =-=[18]-=- and is a special example of a more general class of deterministic IC for which capacity is known [22], including the one-way linear deterministic IC [15]. The work here is also related to one-way ICs... |

292 | Wireless Network Information Flow: A Deterministic Approach
- Avestimehr, Diggavi, et al.
(Show Context)
Citation Context ... the same direction achieves capacity. Nodes transmitting data in opposite directions simultaneously transmit. • We next consider linear deterministic models which model Gaussian channels at high SNR =-=[8]-=- and again ask whether adaptation may increase the capacity regions beyond that of two parallel one-way multi-user channels in the → and ← directions. We will show that it does not for the first two c... |

238 |
The capacity of the Gaussian interference channel under strong interference
- Sato
- 1981
(Show Context)
Citation Context ...on). A symmetric two-way Gaussian IC, as in [9], is said to be in “strong interference” when INR ≥ SNR. The capacity region of one-way Gaussian interference channel in strong interference is given by =-=[37]-=-, and for symmetric channels, the sum-capacity when the interference is strong but not very strong, i.e. SNR ≤ INR ≤ SNR(1 + SNR), may be written as Rsym = R12 + R342 ≤ 1 2 log(1 + SNR+ INR). (47) We ... |

228 | Two-way communication channels
- Shannon
- 1961
(Show Context)
Citation Context ...destinations of messages. This permits them to adapt their channel inputs to their past received signals. Such two-way adaptation was first considered in the point-to-point two-way channel by Shannon =-=[4]-=-. Shannon’s inner and outer bounds [4] are not tight in general, and a general computable1 formula for the capacity region of the point-to-point two-way channel remains open. However, encouragingly, c... |

129 |
The capacity region of a class of deterministic interference channels
- Gamal, Costa
- 1982
(Show Context)
Citation Context ...a matching inner bound for a special class of degraded Z channels are obtained. The capacity region of the one-way deterministic Z channel with invertibility constraints similar in flavor to those in =-=[22]-=-, is found in [23], which will be of use here. The last channel model considered is the two-way linear deterministic IC in which there are 4 messages and 4 terminals forming ICs in the → and ← directi... |

125 |
The capacity of the white gaussian multiple access channel with feedback
- Ozarow
- 1984
(Show Context)
Citation Context ...AC, whose sum-rate is dominated by R12 + R32 ≤ 12 log ( 1 + P1 + P3 N2 ) . (20) For the converse, first consider the MAC direction, and follow steps along the lines of a MAC with feedback as in [19], =-=[34]-=-: n(R12 + R32) = H (M12, M32) = H (M12, M32|M21, M23) (21) = H (M12, M32|M21, M23, Y n2 ) + I (M12, M32; Y n2 |M21, M23) (22) (a)≤ nn + n ∑ i=1 H (Y2,i |Y i−12 , M21, M23) −H (Y2,i |Y i−12 , M12, M32... |

117 |
The capacity region of a channel with two senders and two receivers
- Ahlswede
- 1974
(Show Context)
Citation Context ...+ SNR+ INR). (47) We note that this rate is achievable for the two-way Gaussian IC by using the simultaneous non-unique decoding scheme for the interference channel in strong interference [18], [37], =-=[38]-=-) in the → and ← directions, and noting that any self-interference may be canceled. This non-adaptive scheme which achieves (47) in each direction also achieves to within 1 bit (per user, per directio... |

114 |
The two-user Gaussian interference channel: a deterministic view
- Bresler, Tse
- 2008
(Show Context)
Citation Context ... information as in [5, Corollary 4.1]. The first of our three channel models is a two-way MAC/BC channel. The capacity regions of the linear-deterministic one-way MAC and BC channels were obtained in =-=[15]-=-. An achievable rate region and an outer bound of a similar two-way and adaptive multi-user half-duplex two-way channel is derived in [16] and [17] for Gaussian and discrete memoryless channels (DMC),... |

99 |
A case where interference does not reduce capacity
- Carleial
- 1975
(Show Context)
Citation Context ...SNR(1 + SNR), as in [9, below equation (21)]. It is well known that the capacity region of the one-way Gaussian IC in very strong interference is that of two parallel Gaussian point-to-point channels =-=[36]-=-, which may be achieved by having each receiver first decode the interfering signal, treating its own as noise, subtracting off the decoded interference, and decoding its own message. Given that the i... |

91 |
Directed information for channels with feedback
- Kramer
- 1998
(Show Context)
Citation Context ...ut the use of unbounded cardinality auxiliary random variables. Multi-letter formulas for the capacity of two-way channels exist, see the expressions involving directed information over code-trees of =-=[5]-=-. 0018-9448 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more in... |

70 |
An achievable region and outer bound for the gaussian broadcast channel with feedback
- Ozarow, Leung-Yan-Cheong
- 1984
(Show Context)
Citation Context ... non-negative R21, R23 such that R21 ≤ I (X2; Y1, Y3|U), R23 ≤ I (U ; Y3) (28) over all distributions of the form p(u)p(x2|u)p(y1, y3|x2) p(y3|y1, y3). Evaluation for the Gaussian channel, as done in =-=[35]-=-, yields an outer bound of R21 ≤ 12 log ( 1 + αP2 N1 N1 + N3 N3 ) , R23 ≤ 12 log ( 1 + (1 − α)P2 N3 + αP2 ) (29) for 0 ≤ α ≤ 1. Taking the difference between the sum of the outer bound to the adaptive... |

67 | Feedback capacity of the Gaussian interference channel to within 2 bits
- Suh, Tse
- 2011
(Show Context)
Citation Context ...general class of deterministic IC for which capacity is known [22], including the one-way linear deterministic IC [15]. The work here is also related to one-way ICs with perfect output feedback [24], =-=[25]-=-, with ratelimited feedback [26], with generalized feedback [27], and interfering feedback [24], [28]. In all these channel models only two messages are present and the “feedback” links, whether perfe... |

39 |
The feedback capacity region of a class of discrete memoryless multiple-access channels with feedback
- Willems
- 1982
(Show Context)
Citation Context ...MAC/BC has not been considered, and bears most resemblance to a combined MAC channel with feedback and BC channel with feedback (see references in [18, Ch. 17, Bibliographic Notes], and in particular =-=[19]-=-, [20]), though we note that in our two-way model there are no “free” feedback links–any feedback must travel over the same links as the data in the opposite direction, and hence the MAC and BC with f... |

29 |
A general coding scheme for the two-way channel
- Han
- 1984
(Show Context)
Citation Context ...ar fashion, the capacity of a two-way Gaussian pointto-point channel is equal to two parallel Gaussian channels as shown in Fig. 1(b), which may be achieved without the use of adaptation at the nodes =-=[6]-=-. Similar results are true for twoway additive exponential noise family channels [7]. A note on terminology. In this work, “adaptation” or “interaction” is said to take place when the next channel inp... |

24 | Interference channels with ratelimited feedback - Vahid, Suh, et al. - 2012 |

22 |
Feedback does not increase the capacity of discrete channels with additive noise
- Alajaji
- 1995
(Show Context)
Citation Context ... ON INFORMATION THEORY, VOL. 60, NO. 3, MARCH 2014 conditions somewhat resemble the symmetry structure seen in discrete one-way additive noise channels, where feedback has been shown to be useless in =-=[32]-=-. Theorem 2: The capacity region of the two-way “deterministic, invertible and alphabet restricted” MAC/BC satisfying the conditions P1, P2, P3 is the set of non-negative (R12, R32, R21, R43) satisfyi... |

21 | New outer bounds to capacity regions of two-way channels - Zhang, Berger, et al. - 1986 |

20 |
Gamal, “The feedback capacity of degraded broadcast channels (corresp
- El
- 1978
(Show Context)
Citation Context ... has not been considered, and bears most resemblance to a combined MAC channel with feedback and BC channel with feedback (see references in [18, Ch. 17, Bibliographic Notes], and in particular [19], =-=[20]-=-), though we note that in our two-way model there are no “free” feedback links–any feedback must travel over the same links as the data in the opposite direction, and hence the MAC and BC with feedbac... |

19 | An outer bound region for Interference Channels with Generalized Feedback
- Tuninetti
- 2010
(Show Context)
Citation Context ...2], including the one-way linear deterministic IC [15]. The work here is also related to one-way ICs with perfect output feedback [24], [25], with ratelimited feedback [26], with generalized feedback =-=[27]-=-, and interfering feedback [24], [28]. In all these channel models only two messages are present and the “feedback” links, whether perfect, noisy, or interfering still serve only to further rates in t... |

16 |
Dependence balance bounds for single output two-way channels
- Hekstra, Willems
- 1989
(Show Context)
Citation Context ...complexity in computing this capacity region, it is not entirely satisfying and the capacity region of the two-way channel is generally considered to be open. The binary multiplier channel (BMC) [10]–=-=[14]-=- is a nice example of a deterministic, binary, common output two-way channel where capacity is not exactly known, though its capacity may be expressed in terms of directed information as in [5, Coroll... |

15 | The Z channel
- Vishwanath, Jindal, et al.
- 2003
(Show Context)
Citation Context ...e. The second channel model we consider is the two-way Z channel, with 6 messages. The one-way Z channel (with 3 messages, rather than the Z Interference channel with 2 messages) was first studied in =-=[21]-=-, in which a general outer bound, and a matching inner bound for a special class of degraded Z channels are obtained. The capacity region of the one-way deterministic Z channel with invertibility cons... |

14 | The capacity region of the two-way channel can exceed the inner bound - Dueck - 1979 |

11 | Two-way interference channels
- Suh, Wang, et al.
- 2012
(Show Context)
Citation Context ...rministic IC [15]. The work here is also related to one-way ICs with perfect output feedback [24], [25], with ratelimited feedback [26], with generalized feedback [27], and interfering feedback [24], =-=[28]-=-. In all these channel models only two messages are present and the “feedback” links, whether perfect, noisy, or interfering still serve only to further rates in the forward direction. The only other ... |

10 | On channel output feedback in deterministic interference channels
- Sahai, Aggarwal, et al.
- 2009
(Show Context)
Citation Context ... more general class of deterministic IC for which capacity is known [22], including the one-way linear deterministic IC [15]. The work here is also related to one-way ICs with perfect output feedback =-=[24]-=-, [25], with ratelimited feedback [26], with generalized feedback [27], and interfering feedback [24], [28]. In all these channel models only two messages are present and the “feedback” links, whether... |

7 | The capacity region of a class of deterministic Z channels - Cadambe, Jafar, et al. |

6 | On an extension of an achievable rate region for the binary multiplying channel - Schalkwijk - 1983 |

5 | On the capacity of multi-user two-way linear deterministic channels
- Cheng, Devroye
- 2012
(Show Context)
Citation Context ... 12, 2014. Z. Cheng and N. Devroye were supported by NSF under Award 1053933. This paper was presented at the 2011 Allerton Conference [1], the 2012 IEEE International Symposium on Information Theory =-=[2]-=-, and the 2012 Allerton Conference [3]. The authors are with the University of Illinois at Chicago, Chicago, IL 60607 USA (e-mail: zcheng3@uic.edu; devroye@uic.edu). Communicated by S. Diggavi, Associ... |

5 | An outer bound for a multiuser two-way channel
- Dash, Sabharwal
- 2010
(Show Context)
Citation Context ...ar-deterministic one-way MAC and BC channels were obtained in [15]. An achievable rate region and an outer bound of a similar two-way and adaptive multi-user half-duplex two-way channel is derived in =-=[16]-=- and [17] for Gaussian and discrete memoryless channels (DMC), respectively. In particular, the achievable rate region derived employs adaptation using Block Markov encoding, and the outer bound conta... |

5 | An achievable rate region for a multiuser half-duplex two-way channel
- Dash, Khoshnevis, et al.
- 2006
(Show Context)
Citation Context ...inistic one-way MAC and BC channels were obtained in [15]. An achievable rate region and an outer bound of a similar two-way and adaptive multi-user half-duplex two-way channel is derived in [16] and =-=[17]-=- for Gaussian and discrete memoryless channels (DMC), respectively. In particular, the achievable rate region derived employs adaptation using Block Markov encoding, and the outer bound contains both ... |

5 | constant gaps for the two-way gaussian interference channel - “On - 2012 |

5 | The binary multiplying channel - a coding scheme that operates beyond Shannon’s inner bound region - Schalkwijk - 1982 |

4 | The binary multiplying channel—A coding scheme that operates beyond Shannon’s inner bound region (corresp - Schalkwijk - 1982 |

3 | Multi-user two-way deterministic modulo 2 adder channels – when adaptation is useless
- Cheng, Devroye
- 2011
(Show Context)
Citation Context ...f publication December 20, 2013; date of current version February 12, 2014. Z. Cheng and N. Devroye were supported by NSF under Award 1053933. This paper was presented at the 2011 Allerton Conference =-=[1]-=-, the 2012 IEEE International Symposium on Information Theory [2], and the 2012 Allerton Conference [3]. The authors are with the University of Illinois at Chicago, Chicago, IL 60607 USA (e-mail: zche... |

3 | On constant gaps for the two-way Gaussian interference channel
- Cheng, Devroye
- 2012
(Show Context)
Citation Context ...e supported by NSF under Award 1053933. This paper was presented at the 2011 Allerton Conference [1], the 2012 IEEE International Symposium on Information Theory [2], and the 2012 Allerton Conference =-=[3]-=-. The authors are with the University of Illinois at Chicago, Chicago, IL 60607 USA (e-mail: zcheng3@uic.edu; devroye@uic.edu). Communicated by S. Diggavi, Associate Editor for Shannon Theory. Color v... |

3 | An outer bound region for the parallel two-way channel with interference - Cheng, Devroye - 2011 |

3 | the capacity of multi-user two-way linear deterministic channels - “On - 2012 |

3 | an extension of an achievable rate region for the binary multiplying channel - “On - 1983 |

3 | Two-way interference channels,” arXiv:1202.5014v1 - Suh, Wang, et al. - 2012 |

1 |
Two way communications over exponential family type channels
- Varshney
- 2013
(Show Context)
Citation Context ... parallel Gaussian channels as shown in Fig. 1(b), which may be achieved without the use of adaptation at the nodes [6]. Similar results are true for twoway additive exponential noise family channels =-=[7]-=-. A note on terminology. In this work, “adaptation” or “interaction” is said to take place when the next channel input is a non-trivial function of the node’s past received signals. One may alternativ... |