Toward the optimal multirate multicast for lossy packet network

Multirate multicast is a powerful methodology of multimedia communication in heterogenous networks. A variant of multirate multicast motivated by scalable multimedia streaming is layered multicast, where the transmitted signal is presented in successive data layers. With recent advances of network coding theory, many layered multicast schemes using network coding have been proposed to improve the performance of traditional routing-based layered multicast. They divide the network into different layers and construct a unirate multicast network code for each layer. However, these schemes do not perform network coding between data layers, and consequently cannot realize the full potential of network coding. In this paper, we propose a novel approach to layered multicast that allows network coding of data in different layers. This relaxation lends the proposed scheme greater flexibility in optimizing the data flow than previous layered solutions, and thus achieves higher throughput.

Linear network coding is a promising technology that can maximize the throughput capacity of communication network. Despite this salient feature, there are still many challenges to be addressed, and security is clearly one of the most important challenges. In this paper, we will address the design of secure linear network coding. Specifically, we will investigate the network coding design that can both satisfy the weakly secure requirements and maximize the transmission data rate of multiple unicast streams between the same source and destination pair, which has not been addressed in the literature. In our study, we first prove that the secure unicast routing problem is equivalent to a constrained link-disjoint path problem. We then develop efficient algorithm that can find the optimal unicast topology in a polynomial amount of time. Based on the topology, we design deterministic linear network code that is weakly secure and can be constructed at the source node. And finally, we investigate the potential of random linear code for weakly secure unicast and prove the low bound of the probability that a random linear code is weakly secure.

Network coding has recently been applied to wireless networks and has achieved some initial success. Researches in wireless network coding have been mostly focusing on utilizing the broadcast nature of the wireless networks. In this paper, we propose a novel network coding framework for wireless relay networks that also takes into consideration the fading and error prone nature of the wireless networks. First, we extend the traditional network coding in lossless networks which operates on 0-1 bits, to a new framework which defines network coding on the posterior probability of each bit. This new framework allows an imperfect decode-recode process at a relay node and avoids possible error propagation when a hard decision is made at the relay node. It implicitly integrates decode-and-forward and estimate-and-forward strategies for wireless network coding to address the technical issues of channel fading and transmission errors. The proposed approach is validated through both theoretical analysis and extensive simulations. Both analysis and simulation confirm that this new framework is able to achieve significant gain over traditional network coding. This new framework also enables the introduction of adaptive scheme into network coding. We demonstrate a basic adaptation scheme and present some preliminary experimental results. The proposed adaptive scheme will lay down an essential foundation in this emerging field of wireless network coding in order to address issues related to link heterogeneity.

네트워크 코딩(Network Coding)은 통신망의 성능 향상에 도움을 줄 수 있으나 이의 소프트웨어적 구현은 부호화/복호화 단계에서 매우 큰 지연시간을 유발할 수 있어 이를 줄일 수 있는 병렬화된 구현이 필수적이라 할 수 있다. 본 논문에서는 랜덤 리니어 네트워크 코딩(Random Linear Network Coding)과 랜덤 리니어 네트워크 코딩의 단점을 보완하고자 최근 제안된 파이프라인 네트워크 코딩(Pipeline Network Coding)의 병렬처리 성능을 비교한다. 또한, 네트워크 코딩의 CPU에서의 병렬처리 기법과 GPGPU(General Purpose Graphics Processing Units)에서의 병렬처리 기법을 비교하여 네트워크 코딩의 사용 시 그 파라미터에 따라 적절한 병렬처리 기법을 선택할 필요성이 있음을 보여준다. Network coding has been shown to improve various performance metrics in network systems. However, if network coding is implemented as software a huge time delay may be incurred at encoding/decoding stage so it is imperative for network coding to be parallelized to reduce time delay when encoding/decoding. In this paper, we compare the performance of parallelized decoders for random linear network coding (RLC) and pipeline network coding (PNC), a recent development in order to alleviate problems of RLC. We also compare multi-threaded algorithms on multi-core CPUs and massively parallelized algorithms on GPGPU for PNC/RLC.

Chapter 1 - An Introduction to Network Coding

This paper extends the part of the theory on linear network coding (S.-Y.R. Li et al., 2003) over an acyclic network. The extension also applies to "static linear network code" that is introduced by R. Koetter and M. Medard, (2003). Another objective is the rigorous clarification of fundamental concepts in linear network coding

Recently, it has been proven that retransmission based on Network Coding (NC) can greatly improve the performance of wireless networks with broadcast erasure channels. However, network coding also introduces additional delay at the both sending and receiving sides, resulting in the decline of the Quality of user Experience (QoE). In this paper, we consider the users' waiting time and the decoding delay as the performance metrics and then propose MixCode, a NC-based loss recovery method, to improve the delay performance in heterogeneous wireless networks. MixCode incorporates Opportunistic Network Coding (ONC) with Random Linear Network Coding (RLNC), where a NC packet can be decoded by simply XORing operation at some destinations, but by Gaussian elimination at other destinations. Simulation results show that our proposed algorithm can efficiently reduce both the waiting time and the decoding delay in comparison with the existing NC-based schemes.

In communications networks, the capacity region of multisource network coding is given in terms of the set of entropy functions Gamma*. More broadly, determination of Gamma* would have an impact on converse theorems for multi-terminal problems in information theory. This paper provides several new dualities between entropy functions and network codes. Given a function g ges 0 defined on all subsets of N random variables, we provide a construction for a network multicast problem which is ldquosolvablerdquo if and only if g is the entropy function of a set of quasi-uniform random variables. The underlying network topology is fixed and the multicast problem depends on g only through link capacities and source rates. A corresponding duality is developed for linear network codes, where the constructed multicast problem is linearly solvable if and only if g is linear group characterizable. Relaxing the requirement that the domain of g be subsets of random variables, we obtain a similar duality between polymatroids and the linear programming bound. These duality results provide an alternative proof of the insufficiency of linear (and abelian) network codes, and demonstrate the utility of non-Shannon inequalities to tighten outer bounds on network coding capacity regions.

Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an L-dimensional vector of data symbols over a base field GF(q). There are classical exemplifying multi-source networks that have simple vector linear solutions but no scalar linear solutions over any field. For (single-source) multicast networks, a popular conjecture characterizes the following benefit of vector LNC over scalar LNC in terms of alphabet size of data units: there exist multicast networks that are vector linearly solvable of dimension L over GF(q) but not scalar linearly solvable over any field of size q' ≤ q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> . This paper introduces a general method to construct such a network, and subsequently constructs the first examples to affirm the positive answer of this conjecture. Moreover, among these exemplifying networks vector linearly solvable of dimension L over GF(q), there are instances with the additional property that even for some extremely large q' > q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sup> , they are still not scalar linearly solvable over GF(q').

Energy-efficient relay selection and power allocation for multi-source multicast network-coded D2D communications

Grassmannian codes are known to be useful in error correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet size. The multicast networks which were used for this purpose are generalized combination networks. In both the scalar and the vector network coding solutions, the subspace distance is used as the distance measure for the codes which solve the network coding problem in the generalized combination networks. In this paper, we show that the subspace distance can be replaced with two other possible distance measures which generalize the subspace distance. These two distance measures are shown to be equivalent under an orthogonal transformation. It is proved that the Grassmannian codes with the new distance measures generalize the Grassmannian codes with the subspace distance and the subspace designs with the strength of the design. Furthermore, optimal Grassmannian codes with the new distance measures have minimal requirements for the network coding solutions of some generalized combination networks. The coding problems related to these two distance measures, especially with respect to network coding, are discussed. Finally, by using these new concepts, it is proved that the codes in the Hamming scheme form a subfamily of the Grassmannian codes.

Transmission issue of wireless video, as the hugest percentage among mobile traffics, is a challenge problem in wireless/mobile networks. To tackle video transmission problem occurred in heterogeneous networks as well as different devices, scalable video coding (SVC) has been developed. Also, network coding (NC) enables to transmit efficiently for same given bandwidth. In this paper, we propose a simple random linear network coding (RLNC) for SVC transmission with decode and forward (DF) system over wireless relay network. In order to transmit base layer of SVC with high reliability using characteristics of RLNC in DF relay system, we propose a method which re-groups differently basic coding units of base layer and enhancement layers in SVC. The simulation shows our proposed method gains better performance compared to previous methods.

We propose a novel linear physical-layer network coding (NC) scheme for a fading Y-channel without channel state information at transmitters. In this three-user scheme, each user intends to realize a full data exchange with the other two users via a relay. Instead of directly decoding the users' messages from the received signal, the relay determines NC generator matrices and reconstructs linear NC codewords from its received signals to facilitate the information exchange. We present an explicit solution for NC generator matrices that minimize the NC error probability at high SNRs. We also present and prove an approximation of the NC error probability of the proposed scheme at high SNRs. Numerical results show that the proposed scheme outperforms existing ones, and its performance can be well characterized by the approximation.

Emerging wireless multicast applications simultaneously impose two requirements to the underlying communication networks: to provide sufficient bandwidth and to support a variety of quality-of-service (QoS) sensitivities. For the first requirement, network coding has been proposed recently as an effective way of improving bandwidth utilization. However, almost all previous works about network coding focus on the throughput gain without considering the QoS requirements. Optimal network code construction in wireless multicast under different QoS constraints remains as a significant challenge. In this research, we study the QoS-driven network coding problem. We use large deviation principle to establish the relationship among source rate, link condition, QoS requirement, and network code. Using this relationship, under given QoS requirements, we solve the optimal network code construction problem. The proposed network code supports maximal source rate without violating the QoS requirements. These results constitute the foundations for future designing and implementing network coding based wireless multicast protocols.

Parallel architectures involves parallel communication with the aim of fast receiving of complete information with higher information rate at each nodes. To reduce the complexity of parallel communication we have considered Multi-Mesh of Trees (MMT) architecture for parallel communication and implemented Linear Network Coding (LNC) on MMT by proposing Linear-Code Multicast with Parallel Algorithms (LCM-PA) to achieve max-flow from the source to each receiving nodes. We wish to minimize the communication steps and time complexity involved in transfer of data from processor to processor during parallel communication while achieving the desired throughput in a multicast scenario. We developed a novel distributed parallel network approach, which is enriched by linear coding.