The throughput benefits of random linear network codes have been studied extensively for wirelined and wireless erasure networks. It is often assumed that all nodes within a network perform coding operations. In energy-constrained systems, however, coding subgraphs should be chosen to control the number of coding nodes while maintaining throughput. In this paper, we explore the strategic use of network coding in the wireless packet erasure relay channel according to both throughput and energy metrics. In the relay channel, a single source communicates to a single sink through the aid of a half-duplex relay. The fluid flow model is used to describe the case where both the source and the relay are coding, and Markov chain models are proposed to describe packet evolution if only the source or only the relay is coding. In addition to transmission energy, we take into account coding and reception energies. We show that coding at the relay alone while operating in a rateless fashion is neither throughput nor energy efficient. Given a set of system parameters, our analysis determines the optimal amount of time the relay should participate in the transmission, and where coding should be performed.
In this paper, we explore rateless transmissions, where the acknowledgement for successful reception is sent only once by the destination when the transmission of all available data is completed. As described in the introduction, we also take into account the energy spent on reception and packet processing in addition to the energy required to transmit them. Furthermore, we assume that a sufficiently large field is used for network coding operations, such that transmissions of non-innovative packets from the source can be neglected. In terms of energy use, we make the simple assumption that coding energy stays constant as field size increases, and show that, the decision to code depends on the dominating energy term (transmission, reception, or code generation). The tradeoff between energy budget for the transmission of linearly dependent packets when field size is small and the energy budget for code generation when field size is large is discussed in @cite_4 .
@cite_4
1990808825 2088506000 2952044966 2161586373
Communication over a broadband fading channel powered by an energy harvesting transmitter is studied. Assuming non-causal knowledge of energy data arrivals and channel gains, optimal transmission schemes are identified by taking into account the energy cost of the processing circuitry as well as the transmission energy. A constant processing cost for each active sub-channel is assumed. Three different system objectives are considered: i) throughput maximization, in which the total amount of transmitted data by a deadline is maximized for a backlogged transmitter with a finite capacity battery; ii) energy maximization, in which the remaining energy in an infinite capacity battery by a deadline is maximized such that all the arriving data packets are delivered; iii) transmission completion time minimization, in which the delivery time of all the arriving data packets is minimized assuming infinite size battery. For each objective, a convex optimization problem is formulated, the properties of the optimal transmission policies are identified, and an algorithm which computes an optimal transmission policy is proposed. Finally, based on the insights gained from the offline optimizations, low-complexity online algorithms performing close to the optimal dynamic programming solution for the throughput and energy maximization problems are developed under the assumption that the energy data arrivals and channel states are known causally at the transmitter. In energy harvesting communication systems, an exogenous recharge process supplies energy necessary for data transmission and the arriving energy can be buffered in a battery before consumption. We determine the information-theoretic capacity of the classical additive white Gaussian noise (AWGN) channel with an energy harvesting transmitter with an unlimited sized battery. As the energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: save-and-transmit and best-effort-transmit. In the save-and-transmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the best-effort-transmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory. We consider the optimal online packet scheduling problem in a single-user energy harvesting wireless communication system, where energy is harvested from natural renewable sources, making future energy arrivals instants and amounts random in nature. The most general case of arbitrary energy arrivals is considered where neither the future energy arrival instants or amount, nor their distribution is known. The problem considered is to adaptively change the transmission rate according to the causal energy arrival information, such that the time by which all packets are delivered is minimized. We assume that all bits have arrived and are ready at the source before the transmission begins. For a minimization problem, the utility of an online algorithm is tested by finding its competitive ratio or competitiveness that is defined to be the maximum of the ratio of the gain of the online algorithm with the optimal offline algorithm over all input sequences. We derive a lower and upper bound on the competitive ratio of any online algorithm to minimize the total transmission time in an energy harvesting system. The upper bound is obtained using a lazy' transmission policy that chooses its transmission power to minimize the transmission time assuming that no further energy arrivals are going to occur in future. The lazy transmission policy is shown to be strictly two-competitive. We also derive an adversarial lower bound that shows that competitive ratio of any online algorithm is at least 1.325. A fundamental problem in large scale wireless networks is the energy efficient broadcast of source messages to the whole network. The energy consumption increases as the network size grows, and the optimization of broadcast efficiency becomes more important. In this paper, we study the optimal power allocation problem for cooperative broadcast in dense large-scale networks. In the considered cooperation protocol, a single source initiates the transmission and the rest of the nodes retransmit the source message if they have decoded it reliably. Each node is allocated an-orthogonal channel and the nodes improve their receive signal-to-noise ratio (SNR), hence the energy efficiency, by maximal-ratio combining the receptions of the same packet from different transmitters. We assume that the decoding of the source message is correct as long as the receive SNR exceeds a predetermined threshold. Under the optimal cooperative broadcasting, the transmission order (i.e., the schedule) and the transmission powers of the source and the relays are designed so that every node receives the source message reliably and the total power consumption is minimized. In general, finding the best scheduling in cooperative broadcast is known to be an NP-complete problem. In this paper, we show that the optimal scheduling problem can be solved for dense networks, which we approximate as a continuum of nodes. Under the continuum model, we derive the optimal scheduling and the optimal power density. Furthermore, we propose low-complexity, distributed and power efficient broadcasting schemes and compare their power consumptions with those-of-a traditional noncooperative multihop transmission.