Decodable network coding in wireless network

Network coding is a network layer technique to improve transmission efficiency. Coding packets is especially beneficial in a wireless environment where the demand for radio spectrum is high. However, to fully realize the benefits of network coding two challenging issues that must be addressed are: (1) Guaranteeing separation of coded packets at the destination, and (2) Mitigating the extra coding/decoding delay. If the destination has all the needed packets to decode a coded packet, then separation failure can be averted. If the scheduling algorithm considers the arrival time of coding pairs, then the extra delay can be mitigated. In this paper, we develop a network coding method to address these (decoding and latency) issues for multi-source multi-destination unicast and multicast sessions. We use linear programming to find the most efficient coding design solution with guaranteed decodability. To reduce network delay, we develop a scheduling algorithm to minimize the extra coding/decoding delay. Our coding design method and scheduling algorithm are validated through experiments. Simulation results show improved transmission efficiency and reduced network delay --Abstract, page iii

General Scheme for Perfect Quantum Network Coding with Free Classical Communication

This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with $k$ source-target pairs if there exists a classical linear (or even vector linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of $k$, the maximal fan-in of any network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP'09), LNCS 5555, pp. 622-633, 200

Precoding-Based Network Alignment For Three Unicast Sessions

We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network only performs random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear scheme, which we refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A primary difference between this setting and the wireless interference channel is that the network topology can introduce dependencies between elements of the transfer matrix, which we refer to as coupling relations, and can potentially affect the achievable rate of PBNA. We identify all possible such coupling relations, and interpret these coupling relations in terms of network topology and present polynomial-time algorithms to check the presence of these coupling relations. Finally, we show that, depending on the coupling relations present in the network, the optimal symmetric rate achieved by precoding-based linear scheme can take only three possible values, all of which can be achieved by PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340

On wireless network scheduling with intersession network coding

Abstract—Cross-layer optimization including congestion con-trol, routing, and scheduling has shown dramatic throughput improvement over layered designs for wireless networks. In parallel, the paradigm-shifting network coding has empirically demonstrated substantial throughput improvement when coding operations are permitted at intermediate nodes and packets from different sessions are mixed. Designing network codes and the associated flow in network coding presents new challenges for cross-layer optimization for wireless multi-hop networks. This work shows that with a new flow-based characterization of pairwise intersession network coding, a joint optimal scheduling and rate-control algorithm can be implemented distributively. Optimal scheduling is computationally expensive to achieve even in a purely routing-based (without network coding) paradigm, let alone with network coding. Thus, in this paper, the impact of imperfect scheduling is studied, which shows that pairwise intersession network coding can improve the throughput of routing-based solutions regardless of whether perfect/imperfect scheduling is used. Both the deterministic and stochastic packet arrivals and departures are considered. This work shows for the first time a striking resemblance between pairwise intersession network coding and routing, and thus advocates extensions of routing-based wisdoms to their network coding counterpart. Index Terms—Network coding, pairwise intersession network coding, imperfect scheduling, cross-layer optimization, congestion control. I

Cooperative strategies design based on the diversity and multiplexing tradeoff

This thesis focuses on designing wireless cooperative communication strategies that are either optimal or near-optimal in terms of the tradeoff between diversity and multiplexing gains. Starting from classical cooperative broadcast, multiple-access and relay channels with unit degree of freedom, to more general cooperative interference channels with higher degrees of freedom, properties of different network topologies are studied and their unique characteristics together with several advanced interference management techniques are exploited to design cooperative transmission strategies in order to enhance data rate, reliability or both at the same time. Moreover, various algorithms are proposed to solve practical implementation issues and performance is analyzed through both theoretical verifications and simulations

Linear Network Coding for Two-Unicast-ZZ Networks: A Commutative Algebraic Perspective and Fundamental Limits

We consider a two-unicast-$Z$ network over a directed acyclic graph of unit capacitated edges; the two-unicast-$Z$ network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast-$Z$ networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and non-linear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and Shenvi et. al. regarding feasibility of rate $(1,1)$ in the network.Comment: A short version of this paper is published in the Proceedings of The IEEE International Symposium on Information Theory (ISIT), June 201

Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications

From its introduction to its quindecennial, network coding has built a strong reputation for enhancing packet recovery and achieving maximum information flow in both wired and wireless networks. Traditional studies focused on optimizing the throughput of the system by proposing elaborate schemes able to reach the network capacity. With the shift toward distributed computing on mobile devices, performance and complexity become both critical factors that affect the efficiency of a coding strategy. Instantly decodable network coding presents itself as a new paradigm in network coding that trades off these two aspects. This paper review instantly decodable network coding schemes by identifying, categorizing, and evaluating various algorithms proposed in the literature. The first part of the manuscript investigates the conventional centralized systems, in which all decisions are carried out by a central unit, e.g., a base-station. In particular, two successful approaches known as the strict and generalized instantly decodable network are compared in terms of reliability, performance, complexity, and packet selection methodology. The second part considers the use of instantly decodable codes in a device-to-device communication network, in which devices speed up the recovery of the missing packets by exchanging network coded packets. Although the performance improvements are directly proportional to the computational complexity increases, numerous successful schemes from both the performance and complexity viewpoints are identified