Delay Reduction in Multi-Hop Device-to-Device Communication Using Network Coding

Abstract

This paper considers the problem of reducing the broadcast decoding delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In a D2D configuration, devices in the network can help hasten the recovery of the lost packets of other devices in their transmission range by sending network coded packets. Unlike previous works that assumed fully connected network, this paper proposes a partially connected configuration in which the decision should be made not only on the packet combinations but also on the set of transmitting devices. First, the different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. The joint optimization problem over the set of transmitting devices and the packet combinations of each is, then, formulated. The optimal solution of the joint optimization problem is derived using a graph theory approach by introducing the cooperation graph and reformulating the problem as a maximum weight clique problem in which the weight of each vertex is the contribution of the device identified by the vertex. Through extensive simulations, the decoding delay experienced by all devices in the Point to Multi-Point (PMP) configuration, the fully connected D2D (FC-D2D) configuration and the more practical partially connected D2D (PC-D2D) configuration are compared. Numerical results suggest that the PC-D2D outperforms the FC-D2D and provides appreciable gain especially for poorly connected networks.Index Terms-Instantly decodable network coding, deviceto-device communications, delay reduction, partially connected network, maximum weight clique problem.

A Tutorial on Clique Problems in Communications and Signal Processing

“…In other words, files that are not instantly decodable at the reception timeslots are discarded. These simple properties lead to substantial progress in the design and analysis of IDNC schemes in various network settings [195]- [199]. A survey on the recent advances and applications of IDNC is available in [200].…”

Data Dissemination Using Instantly Decodable Binary Codes in Fog-Radio Access Networks

“…Using the definition of the critical set and the network topology, the problem can be reformulated as a constrained optimization wherein the objective function represents the set of transmitting devices and the constraint the file combinations. Finally, using the expression of the decoding delay provided in [21], the optimization problem is explicitly formulated. The complete proof can be found in Appendix C.…”

“…3) Using the expressions of the decoding delay increment in (C.3) the probability that all the devices in the critical set L do not experience a decoding delay can be expressed as: Under the interference-free transmissions constraint, the authors in [21] show that the optimization over the set of transmitting devices and their file combination can be separated. In other words, the optimization problem is written as:…”

“…Proof: The proof of this preposition is omitted as it mirrors the steps used in proving Lemma 2 in [24].…”

“…However, the authors in [15] propose an efficient on-line decoding delay minimization scheme. This paper suggests using a similar approach by deriving the relationship between the completion time and the decoding delay in the partially connected network of interest and using the decoding delay expressions provided in [21] to obtain an online completion time minimization scheme. The paper's main contribution is to propose an efficient method for disseminating the files among the devices on a partially connected D2D F-RAN.…”