Minimum-energy multicast in mobile ad hoc networks using network coding

• Published in: IEEE transactions on communications Vol. 53; no. 11; pp. 1906 - 1918
• Main Authors: Wu, Y., Chou, P.A., Sun-Yuan Kung
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Broadcasting; Coding; Coding, codes; Computer networks; Costs; Energy efficiency; Equipments and installations; Exact sciences and technology; Information, signal and communications theory; Linearity; Mathematical models; Mobile ad hoc networks; Mobile radiocommunication systems; mobility; multicast; Multicasting; Network coding; Networks; Operations research; Optimization; Pattern recognition; Polynomials; Power generation economics; Pricing; Radiocommunications; Routing; Routing (telecommunications); Signal and communications theory; Signal processing; Steiner tree; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Trees; wireless ad hoc networks; Wireless networks; Cost minimization; mobility; Wireless telecommunication; wireless ad hoc networks; Shape detection; Data broadcast; Information dissemination; Optimization; Multicast; Relaxation; routing; Coding; Energetic efficiency; Information network; Pricing; Minimum energy; Ad hoc network; Mobile radiocommunication; network coding; Steiner tree problem; Polynomial time; Steiner tree; Linearity; Optimal solution; NP hard problem; Network routing; Signal processing; Feature extraction; Energy efficiency; Edge detection
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2005.857148

The minimum energy required to transmit one bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that, under a layered model of wireless networks, the minimum energy-per-bit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energy-per-bit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only allows a potentially lower energy-per-bit to be achieved, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NP-hardness of constructing the minimum-energy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edge-based pricing, where the edge prices are the energy-per-bits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energy-per-bit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energy-per-bit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing.