A sensor is a small electronic device which has the ability to sense, compute and communicate either with other sensors or directly with a base station (sink). In a wireless sensor network (WSN), the sensors monitor a region and transmit the collected data packets through routes to the sinks. In this study, we propose a mixed-integer linear programming (MILP) model to maximize the number of time periods that a WSN carries out the desired tasks with limited energy and budget. Our sink and sensor placement, scheduling, routing with connected coverage (SP SRC) model is the first in the literature that combines the decisions for the locations of sinks and sensors, activity schedules of the deployed sensors, and data flow routes from each active sensor to its assigned sink for connected coverage of the network over a finite planning horizon. The problem is NP-hard and difficult to solve even for small instances. Assuming that the sink locations are known, we develop heuristics which construct a feasible solution of the problem by gradually satisfying the constraints.Then, we introduce search heuristics to determine the locations of the sinks to maximize the network lifetime. Computational experiments reveal that our heuristic methods can find near optimal solutions in an acceptable amount of time compared to the commercial solver CPLEX 12.7.0. Wireless sensor networks (WSNs) are composed of a large number of wireless devices, called sensors, equipped with communication and computing capabilities to monitor a region. A homogeneous WSN consists of identical sensors, whereas the communication and computing capability of the sensors are different in a heterogeneous network. WSNs are applied to various fields of technology thanks to their easy and cheap deployment features. They are used to gather information about human activities in health care, battlefield surveillance in military, monitor wildlife or pollution in environmental sciences, and so on [30].A sensor can collect data within its sensing range, process data as packets and transmit to a base station (sink) either directly or through other sensors which are within its communication range. Sensors consume energy for sensing, receiving data from other sensors and transmitting data to other sensors or a sink. Energy-aware operating is important for a sensor since it has limited battery energy. A sensor can carry out sensing and communicating tasks when it is active and consumes negligible energy in standby mode [13]. A sensor is no more a member of the WSN, when its battery energy depletes.The number of time periods that a WSN operates as desired is its lif etime and depends highly on the limited energy of the sensors. Hence, energy-aware usage of the sensors helps to prolong the network lifetime. The key factors that affect the energy consumption can be listed as follows: locations of the sensors and sinks in the network, schedule of the active or standby periods of the sensors, sink assignments of the sensors and data transmission routes from the sensors to their ...

In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information by adding redundant bits. Low-density parity-check (LDPC) convolutional codes, a member of the LDPC code family, encode the original information to improve error correction capability. In practice these codes are used to decode very long information sequences, where the information arrives in subsequent packets over time, such as video streams. We consider the problem of decoding the received information with minimum error from an optimization point of view and investigate integer programming-based exact and heuristic decoding algorithms for its solution.In particular, we consider relax-and-fix heuristics that decode information in small windows. Computational results indicate that our approaches identify near-optimal solutions significantly faster than a commercial solver in high channel error rates.Our proposed algorithms can find higher quality solutions compared with commonly used iterative decoding heuristics.LDPC Convolutional (LDPC-C) codes, introduced by J. Feltström and Zigangirov in 1999, are preferred to LDPC block codes in decoding for the cases where information is obtained continuously. They can be decoded by sliding window decoders which implement iterative decoding algorithms (such as belief propagation and density evaluation) at each window [19].Although LDPC-C codes provide short-delay and low-complexity in decoding, they are not in communication standards such as WiMax and DVB-S2 yet [20].In this study, we consider LDPC-C codes and propose optimization based sliding window decoders that can give a near optimal decoded codeword for a received vector of practical length (approximately n = 4000) in an acceptable amount of time. The mathematical formulation and proposed decoding algorithms are explained in Section 3. Our proposed decoders can be used in a real-time reliable communication system since they have low decoding latency.Besides, they are applicable in settings such as deep-space communication system due to their 3 high error correction capability.The rest paper is organized as follows: we define the problem in more detail in the next section. Section 3 explains the proposed decoding techniques. We give the corresponding computational results in Section 4. Some concluding remarks and comments on future work appear in Section 5. Problem DefinitionDigital communication systems transmit information from a sender to a receiver over a communication channel. Communication channels are unreliable environments, such as air, that many sender-receiver pairs share. Hence, during transmission some of the transmitted symbols can be lost or their values can change. In coding theory, information is encoded in order to overcome the occurance of such errors during the transmission. Let the information to be sent be represented by a k-bits long sequence u = u 1 u 2 ...u ...

Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low-density parity-check (LDPC) codes can detect and correct transmission errors if one encodes the original information by adding redundant bits. In practice, heuristic iterative decoding algorithms are used to decode the received vector. However, these algorithms may fail to decode if the received vector contains multiple errors. We consider decoding the received vector with minimum error as an integer programming problem and propose a branch-and-price method for its solution. We improve the performance of our method by introducing heuristic feasible solutions and adding valid cuts to the mathematical formulation. Computational results reveal that our branch-priceand-cut algorithm significantly improves solvability of the problem compared to a commercial solver in high channel error rates. Our proposed algorithm can find higher quality solutions than commonly used iterative decoding heuristics.

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