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## The multiple-access channel with causal side information: Independent states

Venue: | IEEE Trans. Inf. Theory |

Citations: | 8 - 2 self |

### Citations

1329 |
Information Theory: Coding Theorems for Discrete Memoryless Channels. Akademiai Kiado
- Csiszar, Korner
- 1981
(Show Context)
Citation Context ...s reached a contradiction because (72j), (72i), and (72a) cannot all hold. G) Proof of Theorem 1: Throughout the achievability proof, we use the definition of typical sequences and typical sets as in =-=[3]-=-. Thus, denote by the number of occurrences of the letter in the -vector . Then, for a given PMF over the finite alphabet , the -typical set is defined as For a joint PMF and a given -vector , the con... |

1044 | The rate-distortion function for source coding with side information at the decoder II
- Wyner
- 1978
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Citation Context ...y region . The next example is such a case. Although Theorem 1 is proved for the discrete memoryless case, we apply it here for the Gaussian model. Extension to continuous alphabets can be done as in =-=[16]-=-. Example 2: Consider the Gaussian MAC where the state is the channel noise (17) and where we impose average power constraints on the inputs (18) The capacity region of this channel when is revealed s... |

375 | Network Information Theory - Gamal, Kim - 2011 |

234 |
Channels with Side Information at the Transmitter
- Shannon
- 1958
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Citation Context ...s. For memoryless single-user channels, revealing the state strictly causally to the encoder does not increase capacity. And if causally, then the problem is solved elegantly using Shannon strategies =-=[13]-=-. (Shannon strategies are also optimal for the degraded broadcast channel [15].) As we shall see, the situation is quite different on the MAC. Strictly causal side information (SI) can increase the ca... |

223 |
Coding for channel with random parameters,” Prob
- Gel’fand, Pinsker
- 1980
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Citation Context ... users. The first model we study is the MAC with strictly causal SI. Since only past (or delayed) samples of the state are known to the encoders, neither binning (as in Gel’fand and Pinsker’s channel =-=[8]-=-) nor Shannon strategies [13] can be employed. Instead, we derive an achievable region based on block Markov coding. The encoders, having access to a common state sequence (from the previous block), c... |

183 |
A coding scheme for additive noise channels with feedback–I: No bandwidth constraint
- Schalkwijk, Kailath
- 1966
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Citation Context ...bility can be demonstrated not only using our inner bound but also by an explicit scheme that is reminiscent of the Schalkwijk–Kailath coding scheme for the single-user Gaussian channel with feedback =-=[12]-=-. Although the users do not have access to each other’s message and no feedback is available, a Schalkwijk–Kailath type algorithm can be devised for this channel, yielding the full-cooperation region ... |

109 |
A coding theorem for multiple access channels with correlated sources
- Slepian, Wolf
- 1973
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Citation Context ...ion G in the Appendix. It is based on a scheme where a lossy version of the state is conveyed to the decoder using Wyner–Ziv compression [17] and block Markov encoding for the MAC with common message =-=[14]-=-. In some cases, the region coincides with the capacity region . The next example is such a case. Although Theorem 1 is proved for the discrete memoryless case, we apply it here for the Gaussian model... |

38 |
Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information
- Steinberg
- 2005
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Citation Context ...to the encoder does not increase capacity. And if causally, then the problem is solved elegantly using Shannon strategies [13]. (Shannon strategies are also optimal for the degraded broadcast channel =-=[15]-=-.) As we shall see, the situation is quite different on the MAC. Strictly causal side information (SI) can increase the capacity region. And in the causal case, the naïve use of Shannon strategies is ... |

37 | The Wyner-Ziv Problem with Multiple Sources
- Gastpar
- 2004
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Citation Context ...ain achievability result for the strictly causal case is the following. Theorem 1: The region is achievable: (12) Proof: The proof is in Appendix E. It is based on distributed Wyner–Ziv source coding =-=[4]-=- and on block-Markov channel coding to transmit the Wyner–Ziv codewords and the messages (data). The channel output serves as SI for the reconstructor in the distributed Wyner–Ziv code. Since the two ... |

26 |
Partial feedback for two-way and broadcast channels
- Dueck
- 1980
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Citation Context ... And in the causal case, the naïve use of Shannon strategies is suboptimal. That, like feedback, strictly causal SI can be beneficial in some memoryless networks can be learned from the work of Dueck =-=[4]-=- on the additive-noise broadcast channel (BC) with feedback. In additive-noise BCs, if we think about the noise as channel state, then providing the encoder with a feedback link Manuscript received Ju... |

25 |
Channel coding in the presence of side information
- Keshet, Steinberg, et al.
- 2007
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Citation Context ...allowing them to trade the rate of one user against the other. The literature on single-user channels and multiterminal networks that are governed by state sequences is vast. For a recent survey, see =-=[5]-=-. The literature on the causal and strictly causal case is more limited. For single-user memoryless channels, the former was solved by Shannon [9] using “Shannon strategies,” and the latter does not i... |

21 | Multiple access channels with states causally known at the transmitters
- Li, Simeone, et al.
- 2013
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Citation Context ...the former was solved by Shannon [9] using “Shannon strategies,” and the latter does not increase capacity. The degraded broadcast channel is addressed in [10]. For follow-up work on our problem, see =-=[8]-=- and Theorem 2 ahead. The rest of this paper is organized as follows. The definitions and main results pertaining to the first scenario, in which the encoders learn the state sequence strictly causall... |

19 | The multiple access channel with causal and strictly causal side information at the encoders - Lapidoth, Steinberg - 2010 |

11 | The multiple access channel with two independent states each known causally to one encoder
- Lapidoth, Steinberg
- 2010
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Citation Context ...e “doublestate” scenario, where the channel is governed by two independent state sequences, each of which is revealed to a different encoder strictly causally. The double-state scenario is studied in =-=[9]-=- and [10]. Here, we only study the case of a single state, which is revealed (causally or strictly causally) to both encoders. It is instructive to consider the additive Gaussian noise MAC, where the ... |

4 | Feedback, cribbing, and causal state-information on the multiple-access channel,” Submitted to - Bracher, Lapidoth - 2013 |

4 |
On Wyner-Ziv networks
- Gastpar
- 2003
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Citation Context ...s block, and since it knows the state of the channel in the previous block, it can compress the pair . Likewise Transmitter 2. Using Gastpar’s results on the compression of correlated sources with SI =-=[6]-=-, we obtain the improved inner bound, which is described in Theorem 2. In this bound, the constraints (25) guarantee that the rates , , and be large enough so that they suffice to describe the sequenc... |

2 | Gamal and Y-H Kim, Network Information Theory - El - 2011 |

1 | state-information on the multiple-access channel M.S - Bracher, Cribbing, et al. - 2012 |