#### DMCA

## On the capacity of the discrete memoryless broadcast channel with feedback (2013)

Venue: | IEEE Trans. Inf. Theory |

Citations: | 15 - 2 self |

### Citations

236 |
A coding theorem for the discrete memoryless broadcast channel
- Marton
- 1979
(Show Context)
Citation Context ...Markov strategy, where in each block the transmitter sends a combination of fresh data and compressed update information pertaining to the data sent in the previous block. Marton’s no-feedback scheme =-=[10]-=-, [11] is used in each block to send the fresh data and the update information, at rates outside the no-feedback capacity region. The update information sent in a block is essentially an efficient los... |

194 |
A First Course in Information Theory.
- Yeung
- 2002
(Show Context)
Citation Context ...t in an improved region compared to Rinner. Remark 3. Recall that for fixed finite alphabets, the Shannon information measures are continuous (say w.r.t. Euclidean distance) in the joint distribution =-=[28]-=-. Fix the channel’s input, output, and feedback alphabets. Then for any fixed choice of (PU0U1U2 , f, PV0V1V2|U0U1U2Ỹ ), the quantities on the righthand side of Inequalities (12) are continuous in PY... |

90 |
An outer bound on the capacity region of the broadcast channel
- Sato
- 1978
(Show Context)
Citation Context ... R0 +R1 +R2 ≤ 3−H(Z0, Z1)−H(Z0, Z2). (15c) Proof. The no-feedback capacity of a DMBC depends on the channel law PY1Y2|X(y1, y2|x) only through the marginal laws PY1|X(y1|x) and PY2|X(y2|x) (see e.g., =-=[27]-=-). We therefore assume in the following that Z2⊸−Z0⊸−Z1. The converse follows then simply by applying the cutset bound to this modified setup. The achievability follows from Marton’s achievable region... |

89 |
The discrete memoryless multiple access channel with partially cooperating encoders
- Willems
- 1983
(Show Context)
Citation Context ...nal is obtained by feeding the time-t input and the corresponding time-t outputs into a memoryless feedback channel. This general form of feedback is commonly referred to as generalized feedback [1], =-=[2]-=-, [3]. For brevity, here we mostly omit the word generalized. It is easily seen that our setup includes noiseless feedback and noisy feedback as special cases. We focus on discrete memoryless broadcas... |

88 |
Capacity results for the discrete memoryless network
- Kramer
- 2003
(Show Context)
Citation Context ..., one of the two outputs is obtained by processing the other output, then the capacity region with noiseless-feedback coincides with the no-feedback capacity region. In contrast, Dueck [5] and Kramer =-=[6]-=- described some specific examples of DMBCs where the noiseless-feedback capacity region exceeds the no-feedback capacity region. In Dueck’s example, the noiseless-feedback capacity region is known. Ho... |

72 |
der Meulen, “A survey of multi-way channels in information theory: 1961-1976
- van
- 1977
(Show Context)
Citation Context ...d feedback, and present a corresponding singleletter achievable region. Subsequently, we analyze two new examples – a generalization of Dueck’s channel [5], and a noisy version of Blackwell’s channel =-=[7]-=- – where our region is shown to exceed the no-feedback capacity region, even in the presence of feedback noise. Our approach is motivated by Dueck’s example [5], and is based on the following idea. Th... |

70 |
Rate distortion when side information may be absent
- Heegard, Berger
- 1985
(Show Context)
Citation Context ...ders. Our achievable region directly leads to an achievable region for this rate-distortion problem, see [22]. Special cases of this rate-distortion problem have been considered by Heegard and Berger =-=[20]-=-, Tian and Diggavi [23], and Steinberg and Merhav [24], and the lossless counterpart by Timo et al. [25], [26]. 5A. Setup and Achievable Region Our setup is parameterized by the tuple (X ,Y1,Y2,V1,V2,... |

56 | On successive refinement for the Wyner-Ziv problem
- Sterinberg, Merhav
(Show Context)
Citation Context ...vable region for this rate-distortion problem, see [22]. Special cases of this rate-distortion problem have been considered by Heegard and Berger [20], Tian and Diggavi [23], and Steinberg and Merhav =-=[24]-=-, and the lossless counterpart by Timo et al. [25], [26]. 5A. Setup and Achievable Region Our setup is parameterized by the tuple (X ,Y1,Y2,V1,V2, PXY1Y2 , PV1|X , PV2|X , n), where • X ,Y1,Y2,V1,V2 a... |

55 |
Source coding for a simple network
- Gray, Wyner
- 1974
(Show Context)
Citation Context ...e sequence. Thus, our problem is a coordination capacity problem [21]. The rate-distortion problem corresponding to our setup is a lossy version of the Gray-Wyner distributed source-coding problem in =-=[19]-=- with additional side-information at the decoders. Our achievable region directly leads to an achievable region for this rate-distortion problem, see [22]. Special cases of this rate-distortion proble... |

48 |
Capacity of a broadcast channel with one deterministic component,”
- Gelfand, Pinsker
- 1980
(Show Context)
Citation Context ... strategy, where in each block the transmitter sends a combination of fresh data and compressed update information pertaining to the data sent in the previous block. Marton’s no-feedback scheme [10], =-=[11]-=- is used in each block to send the fresh data and the update information, at rates outside the no-feedback capacity region. The update information sent in a block is essentially an efficient lossy des... |

48 | Coordination capacity,”
- Cuff, Permuter, et al.
- 2010
(Show Context)
Citation Context ...r-symbol distortion constraints, here, we require that the sequences produced at the decoders are almost jointly-typical with the source sequence. Thus, our problem is a coordination capacity problem =-=[21]-=-. The rate-distortion problem corresponding to our setup is a lossy version of the Gray-Wyner distributed source-coding problem in [19] with additional side-information at the decoders. Our achievable... |

47 | Interference channel with generalized feedback (a.k.a. with source cooperation): part I: achievable region
- Yang, Tuninetti
- 2011
(Show Context)
Citation Context ...s obtained by feeding the time-t input and the corresponding time-t outputs into a memoryless feedback channel. This general form of feedback is commonly referred to as generalized feedback [1], [2], =-=[3]-=-. For brevity, here we mostly omit the word generalized. It is easily seen that our setup includes noiseless feedback and noisy feedback as special cases. We focus on discrete memoryless broadcast cha... |

44 |
Multiple-access channels with different generalized feedback signals,”
- Carleial
- 1982
(Show Context)
Citation Context ...k signal is obtained by feeding the time-t input and the corresponding time-t outputs into a memoryless feedback channel. This general form of feedback is commonly referred to as generalized feedback =-=[1]-=-, [2], [3]. For brevity, here we mostly omit the word generalized. It is easily seen that our setup includes noiseless feedback and noisy feedback as special cases. We focus on discrete memoryless bro... |

42 | Broadcast erasure channel with feedback - capacity and algorithms - Georgiadis, Tassiulas |

27 |
Partial feedback for two-way and broadcast channels
- Dueck
- 1980
(Show Context)
Citation Context ... degraded, i.e., one of the two outputs is obtained by processing the other output, then the capacity region with noiseless-feedback coincides with the no-feedback capacity region. In contrast, Dueck =-=[5]-=- and Kramer [6] described some specific examples of DMBCs where the noiseless-feedback capacity region exceeds the no-feedback capacity region. In Dueck’s example, the noiseless-feedback capacity regi... |

21 | The multiple access channel with causal and strictly causal side information at the encoders,” in
- Lapidoth, Steinberg
- 2010
(Show Context)
Citation Context ... required by the two receivers have a 2large common part. Our scheme has some ideas in common with Lapidoth and Steinberg’s scheme for the MAC with strictly causal stateinformation at the transmitter =-=[12]-=-, [13]. Recently, another single-letter achievable region for general DMBCs with feedback has been proposed [16]1. Comparing the achievable region in [16] to ours however seems difficult. The paper is... |

20 |
Gamal, “The feedback capacity of degraded broadcast channels (corresp
- El
- 1978
(Show Context)
Citation Context ...s, i.e., in the associated set of rate tuples for which reliable communication is possible. Most previous results on DMBCs with feedback focus on the case of noiseless feedback. For example, El Gamal =-=[4]-=- This paper was in part presented at the International Symposium on Information Theory 2010, in Austin, TX, July 2010. O. Shayevitz was with the Information Theory & Applications Center, University of... |

12 | Side-information scalable source coding
- Tian, Diggavi
- 2008
(Show Context)
Citation Context ...gion directly leads to an achievable region for this rate-distortion problem, see [22]. Special cases of this rate-distortion problem have been considered by Heegard and Berger [20], Tian and Diggavi =-=[23]-=-, and Steinberg and Merhav [24], and the lossless counterpart by Timo et al. [25], [26]. 5A. Setup and Achievable Region Our setup is parameterized by the tuple (X ,Y1,Y2,V1,V2, PXY1Y2 , PV1|X , PV2|X... |

11 | The multiple access channel with two independent states each known causally to one encoder
- Lapidoth, Steinberg
- 2010
(Show Context)
Citation Context ...red by the two receivers have a 2large common part. Our scheme has some ideas in common with Lapidoth and Steinberg’s scheme for the MAC with strictly causal stateinformation at the transmitter [12], =-=[13]-=-. Recently, another single-letter achievable region for general DMBCs with feedback has been proposed [16]1. Comparing the achievable region in [16] to ours however seems difficult. The paper is organ... |

6 | An achievable rate region for the broadcast channel with feedback
- Venkataramanan, Pradhan
(Show Context)
Citation Context ...Steinberg’s scheme for the MAC with strictly causal stateinformation at the transmitter [12], [13]. Recently, another single-letter achievable region for general DMBCs with feedback has been proposed =-=[16]-=-1. Comparing the achievable region in [16] to ours however seems difficult. The paper is organized as follows. In Section II, the necessary mathematical background is provided. The channel model is de... |

6 | Equivalence of two inner bounds on the capacity region of the broadcast channel - Liang, Kramer, et al. - 2008 |

4 | Source coding for a simple network with receiver side information
- Timo, Grant, et al.
- 2008
(Show Context)
Citation Context ... [22]. Special cases of this rate-distortion problem have been considered by Heegard and Berger [20], Tian and Diggavi [23], and Steinberg and Merhav [24], and the lossless counterpart by Timo et al. =-=[25]-=-, [26]. 5A. Setup and Achievable Region Our setup is parameterized by the tuple (X ,Y1,Y2,V1,V2, PXY1Y2 , PV1|X , PV2|X , n), where • X ,Y1,Y2,V1,V2 are discrete finite alphabets; • PXY1Y2 is a joint ... |

3 | Capacity of 1-to-k broadcast erasure channel with channel output feedback - Wang |

3 | An achievable region for the discrete memoryless broadcast channel with feedback
- Shayevitz, Wigger
- 2010
(Show Context)
Citation Context ...n|Xn(y n|xn) = n∏ t=1 PY |X(yt|xt) for all yn and xn with PXn(xn) > 0. 1The conference version of [16] has been presented in the same session at ISIT 2010 as the conference version of this paper, see =-=[14]-=- and [15]. We use the notion of typicality as defined in [17]. For a finite alphabet X , a sequence xn ∈ Xn is said to be ǫ-typical with respect to (w.r.t.) a distribution PX on X if |πxn(x) − PX(x)| ... |

3 |
Achievable rates for the broadcast channel with feedback
- Venkataramanan, Pradhan
- 2010
(Show Context)
Citation Context ...xn) = n∏ t=1 PY |X(yt|xt) for all yn and xn with PXn(xn) > 0. 1The conference version of [16] has been presented in the same session at ISIT 2010 as the conference version of this paper, see [14] and =-=[15]-=-. We use the notion of typicality as defined in [17]. For a finite alphabet X , a sequence xn ∈ Xn is said to be ǫ-typical with respect to (w.r.t.) a distribution PX on X if |πxn(x) − PX(x)| ≤ ǫ · PX(... |

2 |
Gamal and Y-.H Kim, “Lecture notes on network information theory
- El
- 2009
(Show Context)
Citation Context ...hown to exceed the no-feedback capacity region, using either noiseless feedback or noisy feedback, in the limit of low feedback noise. II. PRELIMINARIES A. Notations We broadly follow the notation in =-=[17]-=-. In particular, for any real number M > 1, we use the notation [M ] def= {1, . . . , ⌊M⌋}. The set of positive integers is denoted by Z+. Also, we use upper case symbols to denote random variables, e... |

1 |
Source Coding with Side-Information at the Receivers and an Application
- Wigger
(Show Context)
Citation Context ...ay-Wyner distributed source-coding problem in [19] with additional side-information at the decoders. Our achievable region directly leads to an achievable region for this rate-distortion problem, see =-=[22]-=-. Special cases of this rate-distortion problem have been considered by Heegard and Berger [20], Tian and Diggavi [23], and Steinberg and Merhav [24], and the lossless counterpart by Timo et al. [25],... |

1 |
Source Coding for Conditionally Less Noisy Side-Information
- Timo, Oechtering, et al.
- 2012
(Show Context)
Citation Context ... Special cases of this rate-distortion problem have been considered by Heegard and Berger [20], Tian and Diggavi [23], and Steinberg and Merhav [24], and the lossless counterpart by Timo et al. [25], =-=[26]-=-. 5A. Setup and Achievable Region Our setup is parameterized by the tuple (X ,Y1,Y2,V1,V2, PXY1Y2 , PV1|X , PV2|X , n), where • X ,Y1,Y2,V1,V2 are discrete finite alphabets; • PXY1Y2 is a joint probab... |