Optimization-Based Linear Network Coding for General Connections of Continuous Flows

For general connections, the problem of finding network codes and optimizing resources for those codes is intrinsically difficult and little is known about its complexity. Most of the existing solutions rely on very restricted classes of network codes in terms of the number of flows allowed to be coded together, and are not entirely distributed. In this paper, we consider a new method for constructing linear network codes for general connections of continuous flows to minimize the total cost of edge use based on mixing. We first formulate the minimumcost network coding design problem. To solve the optimization problem, we propose two equivalent alternative formulations with discrete mixing and continuous mixing, respectively, and develop distributed algorithms to solve them. Our approach allows fairly general coding across flows and guarantees no greater cost than any solution without network coding.Comment: 1 fig, technical report of ICC 201

Low Density Graph Codes And Novel Optimization Strategies For Information Transfer Over Impaired Medium

Effective methods for information transfer over an imperfect medium are of great interest. This thesis addresses the following four topics involving low density graph codes and novel optimization strategies.Firstly, we study the performance of a promising coding technique: low density generator matrix (LDGM) codes. LDGM codes provide satisfying performance while maintaining low encoding and decoding complexities. In the thesis, the performance of LDGM codes is extracted for both majority-rule-based and sum-product iterative decoding algorithms. The ultimate performance of the coding scheme is revealed through distance spectrum analysis. We derive the distance spectral for both LDGM codes and concatenated LDGM codes. The results show that serial-concatenated LDGM codes deliver extremely low error-floors. This work provides valued information for selecting the parameters of LDGM codes. Secondly, we investigate network-coding on relay-assisted wireless multiple access (WMA) networks. Network-coding is an effective way to increase robustness and traffic capacity of networks. Following the framework of network-coding, we introduce new network codes for the WMA networks. The codes are constructed based on sparse graphs, and can explore the diversities available from both the time and space domains. The data integrity from relays could be compromised when the relays are deployed in open areas. For this, we propose a simple but robust security mechanism to verify the data integrity.Thirdly, we study the problem of bandwidth allocation for the transmission of multiple sources of data over a single communication medium. We aim to maximize the overall user satisfaction, and formulate an optimization problem. Using either the logarithmic or exponential form of satisfaction function, we derive closed-form optimal solutions, and show that the optimal bandwidth allocation for each type of data is piecewise linear with respect to the total available bandwidth. Fourthly, we consider the optimization strategy on recovery of target spectrum for filter-array-based spectrometers. We model the spectrophotometric system as a communication system, in which the information content of the target spectrum is passed through distortive filters. By exploiting non-negative nature of spectral content, a non-negative least-square optimal criterion is found particularly effective. The concept is verified in a hardware implemen

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Compute-and-Forward on a Multi-User Multi-Relay Channel

In this paper, we consider a system in which multiple users communicate with a destination with the help of multiple half-duplex relays. Based on the compute-and-forward scheme, each relay, instead of decoding the users' messages, decodes an integer-valued linear combination that relates the transmitted messages. Then, it forwards the linear combination towards the destination. Given these linear combinations, the destination may or may not recover the transmitted messages since the linear combinations are not always full rank. Therefore, we propose an algorithm where we optimize the precoding factor at the users such that the probability that the equations are full rank is increased and that the transmission rate is maximized. We show, through some numerical examples, the effectiveness of our algorithm and the advantage of performing precoding allocation at the users. Also, we show that this scheme can outperform standard relaying techniques in certain regimes

Distributed Space-Time Coding Based on Adjustable Code Matrices for Cooperative MIMO Relaying Systems

An adaptive distributed space-time coding (DSTC) scheme is proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receive filters and adjustable code matrices are considered subject to a power constraint with an amplify-and-forward (AF) cooperation strategy. In the proposed adaptive DSTC scheme, an adjustable code matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. The effects of the limited feedback and the feedback errors are assessed. Linear MMSE expressions are devised to compute the parameters of the adjustable code matrix and the linear receive filters. Stochastic gradient (SG) and least-squares (LS) algorithms are also developed with reduced computational complexity. An upper bound on the pairwise error probability analysis is derived and indicates the advantage of employing the adjustable code matrices at the relay nodes. An alternative optimization algorithm for the adaptive DSTC scheme is also derived in order to eliminate the need for the feedback. The algorithm provides a fully distributed scheme for the adaptive DSTC at the relay node based on the minimization of the error probability. Simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.Comment: 6 figure