## Capacity of Fading Channels with Channel Side Information (1997)

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Citations: | 399 - 23 self |

### BibTeX

@MISC{Goldsmith97capacityof,

author = {Andrea Goldsmith},

title = {Capacity of Fading Channels with Channel Side Information},

year = {1997}

}

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### Abstract

We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "water-pouring" in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading.

### Citations

8565 |
Elements of information theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...g. Then nR = H(W jfl n ) = H(W jY n ; fl n ) + I(W ; Y n ; fl n ) asH(W jY n ; fl n ) + I(X n ; Y n jfl n ) bs1 + ffl n nR + I(X n ; Y n jfl n ); (26) where a follows from the data processing theorem =-=[14]-=- and the side information assumption, and b follows from Fano's inequality. Let N fl denote the number of times over the interval [0; n] that the channel has fade level fl. Also let S n fl (w) denote ... |

6050 |
A mathematical theory of communication
- Shannon
- 1948
(Show Context)
Citation Context ...!1: (14) Consider a time-invariant AWGN channel with SNR fl j and transmit power oe j . For a given n, let n j = bnp(fl jsfl ! fl j+1 )c = np(fl jsfl ! fl j+1 ) for n sufficiently large. From Shannon =-=[12]-=-, for R j = B log(1 + fl j oe j =S) = B log(fl j =ae 0 ), we can develop a sequence of (2 n j R j ) codes fxw j [k]g n j k=1 ; w j = 1; : : : ; 2 n j R j with average power oe j and error probability ... |

3016 | Convergence of Probability Measures - Billingsley - 1968 |

1483 |
Information Theory and Reliable Communications
- Gallager
- 1968
(Show Context)
Citation Context ..., and coding scheme to the channel variation. The optimal power allocation is a "water-pouring" in time, analogous to the water-pouring used to achieve capacity on frequency-selective fading=-= channels [1, 2]-=-. We show that for i.i.d. fading, using receiver side information only has a lower complexity and the same approximate capacity as optimally adapting to the channel, for the three fading distributions... |

888 |
Information Theory: Coding Theorems for Discrete Memoryless Channels
- Csiszár, Körner
- 1981
(Show Context)
Citation Context ...variant channel under the worst-case fading conditions. More details about the capacity of time-varying channels under these assumptions can be found in the literature on Arbitrarily Varying Channels =-=[7, 8]-=-. The remainder of this paper is organized as follows. The next section describes the system model. The capacity of the fading channel under the different side information conditions is obtained in Se... |

318 | Variable-rate variable-power MQAM for fading channels
- Goldsmith, Chua
- 1997
(Show Context)
Citation Context ...The suboptimal adaptive techniques reduce complexity at a cost of decreased capacity. This tradeoff between achievable data rates and complexity is examined for adaptive and nonadaptive modulation in =-=[3]-=-, where adaptive modulation achieves an average data rate within 7-10dB of the capacity derived herein (depending on the required error probability), while nonadaptive modulation exhibits a severe rat... |

189 | On the capacity of a cellular CDMA system - Gilhousen, Jacobs, et al. - 1991 |

120 |
Convergence of Probability Measures, 2nd ed
- Billingsley
- 1999
(Show Context)
Citation Context ...ust be greater than zero to satisfy (6). So for fixed ffl there exists an M ffl such that Z 1 M ffl +ae0 B log ` fl ae 0 ' p(fl)dfl ! ffl: (23) Moreover, for M fixed, the monotone convergence theorem =-=[13]-=- implies that lim m!1 mM \Gamma1 X j=0 B log ` fl j ae 0 ' p(fl jsfl ! fl j+1 ) = lim m!1 mM \Gamma1 X j=0 Z fl j+1 fl j B log ` fl j ae 0 ' p(fl)dfl = Z M+ae0 ae 0 B log ` fl ae 0 ' p(fl)dfl: (24) Th... |

89 |
Channels with Block Interference
- McEliece, Stark
- 1984
(Show Context)
Citation Context ...der 0 Encoder 1 Encoder N 0 1 N g g g SYSTEM DECODER y [i] y [i] y [i] Decoder Decoder 0 Decoder 1 N N 0 1 x[i] y[i] Figure 2: Multiplexed Coding and Decoding. 3.2 Side Information at the Receiver In =-=[10]-=- it was shown that if the channel variation satisfies a compatibility constraint then the capacity of the channel with side information at the receiver only is also given by the average capacity formu... |

55 | mutual information, and coding for finite-state Markov channels - Goldsmith, Varaiya, et al. - 1996 |

46 |
Vector coding for partial-response channels
- Kasturia, Aslanis, et al.
- 1990
(Show Context)
Citation Context ..., and coding scheme to the channel variation. The optimal power allocation is a "water-pouring" in time, analogous to the water-pouring used to achieve capacity on frequency-selective fading=-= channels [1, 2]-=-. We show that for i.i.d. fading, using receiver side information only has a lower complexity and the same approximate capacity as optimally adapting to the channel, for the three fading distributions... |

40 |
Capacity and Coding for Gilbert-Elliot Channels
- Mushkin, Bar-David
- 1989
(Show Context)
Citation Context ...igher rates [4]. We do not consider the case when the channel fade level is unknown to both the transmitter and receiver. Capacity under this assumption was obtained for the Gilbert-Elliot channel in =-=[5]-=- and for more general Markov channel models in [6]. If the statistics of the channel variation are also unknown, then channels with deep fading will typically have a capacity close to zero. This is be... |

34 |
Wheatley III, "On the capacity of a cellular CDMA system
- Gilhousen, Jacobs, et al.
- 1991
(Show Context)
Citation Context ...ion is just the capacity of an AWGN channel with SNR oe: C(S) = B log [1 + oe] = B log 1 + 1 E[1=fl] : (9) Channel inversion is common in spread spectrum systems with near-far interference imbalances =-=[11]-=-. It is also very simple to implement, since the encoder and decoder are designed for an AWGN channel, independent of the fading statistics. However, it can exhibit a large capacity penalty in extreme... |

33 |
Gaussian arbitrarily varying channels
- Hughes, Narayan
- 1987
(Show Context)
Citation Context ...variant channel under the worst-case fading conditions. More details about the capacity of time-varying channels under these assumptions can be found in the literature on Arbitrarily Varying Channels =-=[7, 8]-=-. The remainder of this paper is organized as follows. The next section describes the system model. The capacity of the fading channel under the different side information conditions is obtained in Se... |

15 | Capacity, mutual information, and coding for finite-state Markov channels
- Goldsmith, Varaiya
- 1996
(Show Context)
Citation Context ...the channel fade level is unknown to both the transmitter and receiver. Capacity under this assumption was obtained for the Gilbert-Elliot channel in [5] and for more general Markov channel models in =-=[6]-=-. If the statistics of the channel variation are also unknown, then channels with deep fading will typically have a capacity close to zero. This is because the data must be decoded without error, whic... |

11 |
Coding Theorems of Information Theory, 2nd ed
- Wolfowitz
- 1964
(Show Context)
Citation Context ...pacity of a particular channel s 2 S, and p(s) denote the probability, or fraction of time, that the channel is in state s. The capacity of this time-varying channel is then given by Theorem 4.6.1 of =-=[9]-=-: C = X s2S C s p(s): (1) We now consider the capacity of the fading channel shown in Figure 1. Specifically, assume an AWGN fading channel with stationary and ergodic channel gain g[i]. It is well kn... |

2 |
Adaptive coded modulation
- Goldsmith, Chua
- 1997
(Show Context)
Citation Context ...d herein (depending on the required error probability), while nonadaptive modulation exhibits a severe rate penalty. Trellis codes can be combined with the adaptive modulation to achieve higher rates =-=[4]-=-. We do not consider the case when the channel fade level is unknown to both the transmitter and receiver. Capacity under this assumption was obtained for the Gilbert-Elliot channel in [5] and for mor... |