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177
An overview of limited feedback in wireless communication systems
 IEEE J. SEL. AREAS COMMUN
, 2008
"... It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channe ..."
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Cited by 198 (40 self)
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It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finiterate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, singleuser, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
The MIMO ARQ channel: Diversitymultiplexingdelay tradeoff
 IEEE Trans. Inf. Theory
, 2006
"... Abstract—In this paper, the fundamental performance tradeoff of the delaylimited multipleinput multipleoutput (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity–multiplexing tradeoff investigated by Zheng and Tse in standard delaylimited MIM ..."
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Cited by 83 (7 self)
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Abstract—In this paper, the fundamental performance tradeoff of the delaylimited multipleinput multipleoutput (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity–multiplexing tradeoff investigated by Zheng and Tse in standard delaylimited MIMO channels with coherent detection to the ARQ scenario. We establish the threedimensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in longterm static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be
Fifty Years of Shannon Theory
, 1998
"... A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication. ..."
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Cited by 49 (1 self)
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A brief chronicle is given of the historical development of the central problems in the theory of fundamental limits of data compression and reliable communication.
Feedback capacity of stationary Gaussian channels
"... The capacity of stationary additive Gaussian noise channels with feedback is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the firstorder autoregressive movingaverage noise spectrum, ..."
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Cited by 44 (10 self)
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The capacity of stationary additive Gaussian noise channels with feedback is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the firstorder autoregressive movingaverage noise spectrum, this variational characterization yields a closedform expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk–Kailath coding scheme achieves the feedback capacity for the firstorder autoregressive movingaverage Gaussian channel, resolving a longstanding open problem studied by Butman, Schalkwijk– Tiernan, Wolfowitz, Ozarow, Ordentlich, Yang–Kavčić–Tatikonda, and others. 1 Introduction and
The Necessity and Sufficiency of Anytime Capacity for Control over a Noisy Communication Link: Parts I and II
"... We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity cal ..."
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Cited by 38 (6 self)
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We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. The rate required is given by the log of the system gain and the sense of reliability required comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback. In cases of sufficiently...
On reliability of Gaussian channels with noisy feedback
 in Proc. 44th Annu. Allerton Conf. Communication, Control, and Computing
, 2006
"... tsachy @ stanford.edu Abstract Upper and lower bounds are derived on the reliability function of the additive white Gaussian noise channel with output fed back to the transmitter over an independent additive white Gaussian noise channel. Special attention is paid to the regime of very low feedback ..."
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Cited by 34 (6 self)
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tsachy @ stanford.edu Abstract Upper and lower bounds are derived on the reliability function of the additive white Gaussian noise channel with output fed back to the transmitter over an independent additive white Gaussian noise channel. Special attention is paid to the regime of very low feedback noise variance and it is shown that the reliability function is asymptotically inversely proportional to the feedback noise variance. This result shows that the noise in the feedback link, however small, renders the commnication with noisy feedback fundamentally different from the perfect feedback case. For example, it is demonstrated that with noisy feedback, linear coding schemes fail to achieve any positive rate. In contrast, an asymptotically optimal coding scheme is devised, based on a threephase detection/retransmission protocol, which achieves an error exponent inversely proportional to the feedback noise variance for any rate less than capacity.
Feedback capacity of the firstorder moving average Gaussian channel
 IEEE TRANS. INFORM. THEORY
, 2006
"... Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the firstorder autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and more rec ..."
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Cited by 25 (2 self)
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Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the firstorder autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and more recently, Yang, Kavčić, and Tatikonda. Here we consider another simple special case of the stationary firstorder moving average additive Gaussian noise channel and find the feedback capacity in closed form. Specifically, the channel is given by = + =12... where the input satisfies a power constraint and the noise is a firstorder moving average Gaussian process defined by = 1 + 1 with white Gaussian innovations =0 1... We show that the feedback capacity of this channel is. We wish to communicate a message index reliably over the channel. The channel output is causally fed back to the transmitter. We specify a code with the codewords1 satisfying the expected power constraint The proband decoding function ability of error is defined by FB = log 0 where 0 is the unique positive root of the equation
Why block length and delay are not the same thing
 IEEE Trans. Inform. Theory, submitted. [Online]. Available: http://www.eecs.berkeley.edu/ ∼ \protect\kern+.1667em\relax$\protect\kern.1667em\relax$sahai/Papers/FocusingBound.pdf
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Dynamic information and constraints in source and channel coding
, 2004
"... explore dynamics in source coding and channel coding. We begin by introducing the idea of distortion side information, which does not directly depend on the source but instead affects the distortion measure. Such distortion side information is not only useful at the encoder but under certain conditi ..."
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Cited by 23 (4 self)
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explore dynamics in source coding and channel coding. We begin by introducing the idea of distortion side information, which does not directly depend on the source but instead affects the distortion measure. Such distortion side information is not only useful at the encoder but under certain conditions knowing it at the encoder is optimal and knowing it at the decoder is useless. Thus distortion side information is a natural complement to WynerZiv side information and may be useful in exploiting properties of the human perceptual system as well as in sensor or control applications. In addition to developing the theoretical limits of source coding with distortion side information, we also construct practical quantizers based on lattices and codes on graphs. Our use of codes on graphs is also of independent interest since it highlights some issues in translating the success of turbo and LDPC codes into the realm of source coding. Finally, to explore the dynamics of side information correlated with the source, we consider fixed lag side information at the decoder. We focus on the special case of perfect side information with unit lag corresponding to source coding with feedforward (the dual
Coding for the feedback Gel'fandPinsker channel and the feedforward WynerZiv source
 IEEE Trans. Inf. Theory
, 2006
"... We consider both channel coding and source coding, with perfect past feedback/feedforward, in the presence of side information. It is first observed that feedback does not increase the capacity of the Gel’fand–Pinsker channel, nor does feedforward improve the achievable ratedistortion performance i ..."
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Cited by 22 (5 self)
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We consider both channel coding and source coding, with perfect past feedback/feedforward, in the presence of side information. It is first observed that feedback does not increase the capacity of the Gel’fand–Pinsker channel, nor does feedforward improve the achievable ratedistortion performance in the WynerZiv problem. We then focus on the Gaussian case showing that, as in the absence of side information, feedback/feedforward allows to efficiently attain the respective performance limits. In particular, we derive schemes via variations on that of Schalkwijk and Kailath. These variants, which are as simple as their origin and require no binning, are shown to achieve, respectively, the capacity of Costa’s channel, and the WynerZiv rate distortion function. Finally, we consider the finitealphabet setting and derive schemes for both the channel and the source coding problems that attain the fundamental limits, using variations on schemes of Ahlswede and Ooi and Wornell, and of Martinian and Wornell, respectively.