Capacity Theorems for the “Z” Channel

Chong, Hon-Fah; Motani, Mehul; Garg, H.K.

doi:10.1109/tit.2006.890779

Cited by 41 publications

(44 citation statements)

References 11 publications

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“…These can be easily extrapolated to other Z channels by first writing them in a form similar to the Z(21) and substituting for the corresponding variables. For the Z channel, different types of degradation can be defined as in [14]. We focus on type I and type II degradations below [14].…”

Section: Z Channelsmentioning

confidence: 99%

“…For the Z channel, different types of degradation can be defined as in [14]. We focus on type I and type II degradations below [14]. Definition 1.…”

Section: Z Channelsmentioning

confidence: 99%

“…We define a ZC to be degraded of type II if [14] that this class of degraded ZCs is equivalent to the condition that |h 12 | 2 ≥ |h 22 | 2 and the symbol x 2 received at receiver 2 is a degraded version of x 2 received at receiver 1.…”

Section: Z Channelsmentioning

confidence: 99%

“…In [14], an outer bound to the capacity region of the type II degraded Gaussian ZC is determined, which we state below. Theorem 2 (Chong et al).…”

Section: Z Channelsmentioning

confidence: 99%

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Capacity bounds for the Gaussian X channel

Prasad

Chockalingam

2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-We consider bounds for the capacity region of the Gaussian X channel (XC), a system consisting of two transmitreceive pairs, where each transmitter communicates with both the receivers. We first classify the XC into two classes, the strong XC and the mixed XC. In the strong XC, either the direct channels are stronger than the cross channels or vice-versa, whereas in the mixed XC, one of the direct channels is stronger than the corresponding cross channel and vice-versa. After this classification, we give outer bounds on the capacity region for each of the two classes. This is based on the idea that when one of the messages is eliminated from the XC, the rate region of the remaining three messages are enlarged. We make use of the Z channel, a system obtained by eliminating one message and its corresponding channel from the X channel, to bound the rate region of the remaining messages. The outer bound to the rate region of the remaining messages defines a subspace in R 4 + and forms an outer bound to the capacity region of the XC. Thus, the outer bound to the capacity region of the XC is obtained as the intersection of the outer bounds to the four combinations of the rate triplets of the XC. Using these outer bounds on the capacity region of the XC, we derive new sum-rate outer bounds for both strong and mixed Gaussian XCs and compare them with those existing in literature. We show that the sum-rate outer bound for strong XC gives the sum-rate capacity in three out of the four sub-regions of the strong Gaussian XC capacity region. In case of mixed Gaussian XC, we recover the recent results in [11] which showed that the sum-rate capacity is achieved in two out of the three sub-regions of the mixed XC capacity region and give a simple alternate proof of the same.

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Section: Z Channelsmentioning

confidence: 99%

“…For the Z channel, different types of degradation can be defined as in [14]. We focus on type I and type II degradations below [14]. Definition 1.…”

Section: Z Channelsmentioning

confidence: 99%

Section: Z Channelsmentioning

confidence: 99%

“…In [14], an outer bound to the capacity region of the type II degraded Gaussian ZC is determined, which we state below. Theorem 2 (Chong et al).…”

Section: Z Channelsmentioning

confidence: 99%

See 2 more Smart Citations

Capacity bounds for the Gaussian X channel

Prasad

Chockalingam

2013

2013 Information Theory and Applications Workshop (ITA)

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“…Since we assume that node B is much farther away from the other nodes, we do not explicitly consider the interference that node C causes at node B. Since node D receives a combination of both the intended signal from node C and the interfering signal from node A and node B is interference free, this system model is sometimes also referred to as a Z-interference channel (ZIC) [1]- [4], a "Z" channel [5], [6], or a one-sided interference channel. Since we also assumed that node A's signal is cognitively known at node C, we call the network in Fig.…”

Section: Introductionmentioning

confidence: 99%

Capacity Bounds for a Cognitive MIMO Gaussian Z-Interference Channel

Peng

Rajan

2010

IEEE Trans. Veh. Technol.

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Abstract-In this paper, we compute an achievable rate of a multiple-input-multiple-output (MIMO) Gaussian Z-interference channel (ZIC), as shown in Fig. 1, when transmit node C has imperfect cognitive knowledge of the signal sent by transmit node A. First, we compute the capacity of this channel, assuming noncausal but noisy knowledge at node C of node A's signal. We then compute the achievable rate for a causal cognitive strategy: This achievable rate is derived using a two-phase transmission scheme, in which node C uses a combination of a linear MMSE (LMMSE) estimator and a dirty-paper code, and node D employs a combination of an LMMSE estimator and a partial interference canceler. The achievable rate is studied in two different cases: 1) Node C operates in full-duplex mode, and 2) node C operates in half-duplex mode. To quantify the performance of the proposed strategy, we compute simple lower and upper bounds on the capacity of this channel. Similar to an interference channel, the achievable rate of the cognitive ZIC nonmonotonically varies with the interference. Specifically, the achievable rate first decreases with the channel gain between nodes A and D and then begins to increase beyond a certain threshold. The difference in the achievable rate between full-and half-duplex transmissions is also numerically evaluated.Index Terms-Achievable rate, dirty-paper coding (DPC), interference mitigation, random-coding error exponent.

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A bibliometric analysis of publications by the School of Biological Sciences, Seoul National University, South Korea

Kim

2013

Scientometrics

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Capacity Theorems for the “Z” Channel

Cited by 41 publications

References 11 publications

Capacity bounds for the Gaussian X channel

Capacity bounds for the Gaussian X channel

Capacity Bounds for a Cognitive MIMO Gaussian Z-Interference Channel

A bibliometric analysis of publications by the School of Biological Sciences, Seoul National University, South Korea

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