Capacity region of the deterministic multi-pair bi-directional relay network

Avestimehr, Salman; Khajehnejad, Amin; Sezgin, Aydin; Hassibi, Babak

doi:10.1109/itwnit.2009.5158541

Cited by 37 publications

(76 citation statements)

References 13 publications

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“…While user 2 and user 3 transmit message send symbols s [2] c and s [3] c along with precoding vectors v …”

Section: Four User Case (K = 4)mentioning

confidence: 99%

“…The proposed common messages precoding strategy is aiming at obtaining three network coding messages with chain property, W [1] c ⊕ W [2] c , W [2] c ⊕ W [3] c , W [3] c ⊕ W [4] c at the relay. All users carefully choose the precoding vectors in order to satisfy the conditions of signal [2] s v [1,3] …”

Section: Four User Case (K = 4)mentioning

confidence: 99%

“…c,π (3,4) = W [3] c ⊕W [4] c are then obtained by applying the physical-layer network coding (PNC) modulation-demodulation mapping principle into each symbol s p,π (1,2) …”

Section: Four User Case (K = 4)mentioning

confidence: 99%

“…Therefore, the conclusion is that all users are able to detect symbols by ZF detection, which nulls out the inter-signal space interference. For user 1, the detected signal is [1] (8) After self-interference cancellation, user 1 gets the three desired private messages coming from user 2, user 3 and user 4, i.e., s [1,2] p , s [1,3] p and s [1,4] p , and the three encrypted common messages. The decryption procedure is performed by successive network code decoding scheme.…”

Section: Four User Case (K = 4)mentioning

confidence: 99%

“…It has been recently generalized to include multiple links. The authors in [2] studied the relay-aided multi-pair communication network, where a relay node facilitates the communication between multiple pairs of users. Multiuser and multi-way relay communications were considered in [3,4], where multiple users intend to exchange information with a shared relay terminal.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Transmission Scheme for Mimo Y Channel

Wang¹,

Li²,

Li³

et al. 2013

PIER C

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Abstract-This paper proposes a novel scheme for a multi-way communication where users combine bi-directional multi-pair messages exchange with multi-directional multi-pair exchange. Particularly, we focus on the system where multiple users have multiple antennas exchange both private and common messages with each other. In this scheme, we can use simple zero forcing combined with successive network code decoding enables all user to decipher the encryption message from the relay despite the fact that they all have different self-information which they use as a key.

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“…While user 2 and user 3 transmit message send symbols s [2] c and s [3] c along with precoding vectors v …”

Section: Four User Case (K = 4)mentioning

confidence: 99%

Section: Four User Case (K = 4)mentioning

confidence: 99%

“…c,π (3,4) = W [3] c ⊕W [4] c are then obtained by applying the physical-layer network coding (PNC) modulation-demodulation mapping principle into each symbol s p,π (1,2) …”

Section: Four User Case (K = 4)mentioning

confidence: 99%

Section: Four User Case (K = 4)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized Transmission Scheme for Mimo Y Channel

Wang¹,

Li²,

Li³

et al. 2013

PIER C

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Using network coding to achieve the capacity of deterministic relay networks with relay messages

Zewail

Mohasseb

Nafie

et al. 2016

Wireless Communications

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In this paper, we derive the capacity of the deterministic relay networks with relay messages. We consider a network that consists of five nodes, four of which can only communicate via the fifth one. However, the fifth node is not merely a relay as it may exchange private messages with the other network nodes. First, we develop an upper bound on the capacity region based on the notion of a single-sided genie. In the course of the achievability proof, we also derive the deterministic capacity of a four-user relay network (without private messages at the relay). The capacity achieving schemes use a combination of two network coding techniques: the simple ordering scheme and detour scheme. In the simple ordering scheme, we order the transmitted bits at each user such that the bi-directional messages will be received at the same channel level at the relay, while the basic idea behind the detour scheme is that some parts of the message follow an indirect paths to their respective destinations. This paper, therefore, serves to show that user cooperation and network coding can enhance throughput, even when the users are not directly connected to each other. Finally, we make a conjecture about the capacity region of the general K-node relay network with relay messages.A. Zewail et al.The capacity of deterministic relay networks with relay messages the relay just re-orders the received equations created from the superposition of the transmitted signals on the wireless medium and forwards them. We call this scheme the simple ordering scheme (SOS). Then, from the insights of this work, the authors of [7] used a combination of lattice codes and random Gaussian codes at the source nodes to propose a coding scheme that achieves to within 2 bits per user of the cut-set upper bound on the capacity of the two-pair two-way relay network.Reference [8] studied the two-way X-Channel. First, a new upper bound based on the notion of a single-sided genie was developed, then it was used to characterize the deterministic multicast capacity of their network. To prove the achievability, the authors proposed the idea of Detour Schemes that route some bits intended for a certain receiver via alternative paths when they cannot be accommodated on direct routes. Thereafter, the capacity of the deterministic Y-channel was defined in [9]. Building on this result, the authors investigated the capacity of the Gaussian Ychannel in [10]. Then, we extended these works in [11], by considering a four-user relay network with no direct link, where each user wishes to exchange a number of private messages with the other three users via the relay node. Achievability of the capacity region was demonstrated via two detour schemes (DS), which are different from the ones used in [8] because of the different nature of the multicast network. After that, in [12], we studied the capacity of a three-user relay network where the relay node is interested in exchanging some private messages with the other network users. It was shown that, if all messages emanating from ...

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Bidirectional multi-pair network with a MIMO relay: Beamforming strategies and lack of duality

Sezgin

Boche

Avestimehr

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We address the problem of a multi-user relay network, where multiple single-antenna node pairs want to exchange information by using a multiple antenna relay node. Due to the half-duplex constraint of the relay, the exchange of information takes place in two steps. In the first step, the nodes transmit their data to the relay, while in the second step, the relay is broadcasting the data by using linear and non-linear precoding strategies. We focus on the second step in this paper. We first consider the problem of maximizing the overall rate achievable using linear and dirty-paper type precoding strategies at the relay. Then, we consider minimizing the total power at the relay subject to individual SINR constraints using the same strategies at the relay. We show that the downlink-uplink duality does not hold for the setup considered here, which is a somewhat surprising result. We also show that the beamforming strategy which is optimal in the single-pair case performs very well in the multi-pair case for practically relevant SNR. The results are illustrated by numerical simulations.

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Capacity region of the deterministic multi-pair bi-directional relay network

Cited by 37 publications

References 13 publications

Generalized Transmission Scheme for Mimo Y Channel

Generalized Transmission Scheme for Mimo Y Channel

Using network coding to achieve the capacity of deterministic relay networks with relay messages

Bidirectional multi-pair network with a MIMO relay: Beamforming strategies and lack of duality

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