Browsing by Author "Shamai (Shitz), Shlomo"

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On Capacity of the Dirty Paper Channel with Fading Dirt in the Strong Fading Regime
(2014-01-01)
Rini, Stefano
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Shamai (Shitz), Shlomo
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交大名義發表
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National Chiao Tung University
The classic "writing on dirty paper" capacity result establishes that full state pre-cancellation can be attained in Gelfand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumption that both the transmitter and the receiver have perfect knowledge of the channel. We are interested in characterizing capacity under the more realistic assumption that only partial channel knowledge is available at the transmitter. To this end we study the "dirty paper channel with slow fading dirt", a variation of the dirty paper channel in which the state sequence is multiplied by a slow fading value known only at the receiver. For this model we establish two approximate characterizations of capacity, one for the case in which fading takes only two values and one for the case in which fading takes M possible values but these values are greatly spaced apart. For both results, a naive strategy in which the encoder pre-codes against different fading realizations in different time slots is sufficient to approach capacity.
On the Capacity of the Carbon Copy onto Dirty Paper Channel
(2017-09-01)
Rini, Stefano
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Shamai (Shitz), Shlomo
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電機工程學系
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Department of Electrical and Computer Engineering
The "carbon copy onto dirty paper" (CCDP) channel is the compound "writing on dirty paper" channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: 1) the state sequences are independent and identically distributed; and 2) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing, and Gel'fand-Pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within 4 bits per channel use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters, which we denote as "strong fading" regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.
On the Capacity of the Carbon Copying onto Dirty Paper Channel
(2016)
Rini, Stefano
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Shamai (Shitz), Shlomo
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交大名義發表
;
National Chiao Tung University
Costa\'s "writing on dirty paper" capacity result establishes that full state pre-cancellation can be attained in the Gel\'fand-Pinsker channel with additive state and additive Gaussian noise. The "carbon copy onto dirty paper" channel is the extension of Costa\'s model to the compound setting: here a common message is to be decoded at M receivers, each observing the sum of the channel input, Gaussian noise and one of M possible state sequences. As in the Gel\'fand-Pinsker channel, the state sequences are anti-causally known at the encoder, which can thus pre-code its transmissions so as to minimize the adverse effects of the channel states. In this paper we derive the capacity to within 2.25 bits-per-channel-use of the M-user "carbon copying onto dirty paper" channel in which the state sequences are Gaussian distributed with the same variance and the same pairwise correlation.
On the Capacity of the Dirty Paper Channel with Fast Fading and Discrete Channel States
(2016)
Rini, Stefano
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Shamai (Shitz), Shlomo
;
交大名義發表
;
National Chiao Tung University
Interference pre-cancellation as in the "writing onto dirty paper" channel crucially depends on the transmitter having exact knowledge of the way in which input and channel state combine to produce the channel output. The presence of even a small amount of uncertainty in such knowledge, gravely hampers the ability of the encoder to pre-code its transmissions against the channel state. This is particularly disappointing as it implies that interference pre-coding in practical systems is effective only when the channel estimates have very high precision, a condition which is generally unattainable in wireless environments. In this paper we show that state decoding, instead of state pre-cancellation, can be approximately optimal for a channel with discrete states when only partial channel knowledge is available. More specifically, we consider a variation of the "writing onto dirty paper" channel in which a discrete-valued state sequence is multiplied by a fast fading process and derive conditions on the fading distribution for which state decoding closely approaches capacity. This channel model is a special case of the Gelf\'and-Pinsker channel and our results show an instance of this problem in which state decoding is approximately optimal.
On the Dirty Paper Channel with Fast Fading Dirt
(2015)
Rini, Stefano
;
Shamai (Shitz), Shlomo
;
交大名義發表
;
National Chiao Tung University
Costa\'s "writing on dirty paper" result establishes that full state pre-cancellation can be attained in the Gel\'fand-Pinsker problem with additive state and additive white Gaussian noise. This result holds under the assumptions that full channel knowledge is available at both the transmitter and the receiver. In this work we consider the scenario in which the state is multiplied by an ergodic fading process which is not known at the encoder. We study both the case in which the receiver has knowledge of the fading and the case in which it does not: for both models we derive inner and outer bounds to capacity and determine the distance between the two bounds when possible. For the channel without fading knowledge at either the transmitter or the receiver, the gap between inner and outer bounds is finite for a class of fading distributions which includes a number of canonical fading models. In the capacity approaching strategy for this class, the transmitter performs Costa\'s pre-coding against the mean value of the fading times the state while the receiver treats the remaining signal as noise. For the case in which only the receiver has knowledge of the fading, we determine a finite gap between inner and outer bounds for two classes of discrete fading distribution. The first class of distributions is the one in which there exists a probability mass larger than one half while the second class is the one in which the fading is uniformly distributed over values that are exponentially spaced apart. Unfortunately, the capacity in the case of a continuous fading distribution remains very hard to characterize.
The approximate capacity for the 3-receiver writing on random dirty paper channel
(2017-01-01)
Rini, Stefano
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Shamai (Shitz), Shlomo
;
交大名義發表
;
National Chiao Tung University
In this paper, the approximate capacity of the 3-receiver "writing on random dirty paper" (WRDP) channel is derived. In the M-receiver WRDP channel, the channel output is obtained as the sum of the channel input, white Gaussian noise and a channel state sequence randomly selected among a set of M independent Gaussian sequences. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which one is selected to produce the channel output. In the following, we derive upper and lower bounds to the capacity of the 3-receiver WRDP channel which are to within a distance of at most 3 bits-per-channel-use (bpcu) for all channel parameters. In the achievability proof, the channel input is composed of the superposition of three codewords: the receiver opportunistically decodes a different set of codewords, depending on the variance of the channel state appearing in the channel output. Time-sharing among multiple transmission phases is employed to guarantee that transmitted message can be decoded regardless of the state realization. In the converse proof, we derive a novel outer bound which matches the pre-log coefficient arising in the achievability proof due to time-sharing. Although developed for the case of three possible state realizations, our results can be extended the general WRDP.