Trying Linear Network Coding on a Network Flow Processor

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.

In a classical network, data streams originating from a source and intended to a desired destination are routed through intermediate nodes before reaching their final destination. By contrast, Network Coding (NC) manipulates at an intermediate node those data streams by combining the data from the streams before forwarding it to the destination. This paper describes the advances of NC in wireless communication for IMT-Advanced and beyond. A short overview of NC in wireless communications is given first. Afterward, the application of NC to broadcasting is described. Thereafter, NC methods in uplink wireless communications, such as User Grouping (UG) and Relay Selection (RS) are described. Further, the advantage of non-binary over binary network NC is shown in a multi-user multi-relay scenario. Finally the performance of NC is analyzed. In particular, in the uplink Multiple Access Relay Channel (MARC) scenario, the joint UG and RS methods lift the system capacity by 70%. The non-binary NC improves the SNR up to 4 dB. Finally the efficient broadcast method yields up to 22% overhead reduction compared to ARQ.

Network coding is proved to improve the throughput, decrease network latency and balance the network overhead. Combined with wireless overhearing, some proposed representative schemes on network coding, such as linear network coding and Completely opportunity encoding (COPE). The former scheme is based on complicated linear operation, while the latter is implemented by the way of pairwise XOR-ing which is simple and low efficiency. In order to resolve these problems, we put forward a group-based XOR-ing network coding scheme, which has the characteristics of high efficiency and low complexity. Experimental results and theoretical analysis demonstrate that our scheme has higher throughput gains and lower delay than traditional schemes. In addition, our proposed scheme has the best characteristic of fairness among the state-of-the-art approaches.

Chapter 1 - An Introduction to Network Coding

Network coding designs over GF(q) spans an extensive range of research directions covering a wide range of applications. Galois field used for network coding should be a function of the total number of nodes in the networks. Thus, the larger the number of sources and relays the larger the Galois field, while keeping the same diversity order in relay-aided transmission. Furthermore, the modulation order and the Galois field are the same and this solution introduces a constraint on achievable rate and decoding complexity as network code and modulation cannot be chosen independently. In order to overcome this important limitation, in this paper we propose a splitting based approach where network coding and modulation are not necessarily the same. Our results show that if the modulation order is smaller than the Galois field; we are still able to achieve the same diversity order with lower decoding complexity.

Network Coding encourages information coding across a communication network. While the necessity, benefit and complexity of network coding are sensitive to the underlying graph structure of a network, existing theory on network coding often treats the network topology as a black box, focusing on algebraic or information theoretic aspects of the problem. This work aims at an in-depth examination of the relation between algebraic coding and network topologies. We mathematically establish a series of results along the direction of: if network coding is necessary/beneficial, or if a particular finite field is required for coding, then the network must have a corresponding hidden structure embedded in its underlying topology, and such embedding is computationally efficient to verify. Specifically, we first formulate a meta-conjecture, the NC-Minor Conjecture, that articulates such a connection between graph theory and network coding, in the language of graph minors. We next prove that the NC-Minor Conjecture is almost equivalent to the Hadwiger Conjecture, which connects graph minors with graph coloring. Such equivalence implies the existence of K4, K5, K6, and KO(q/ log q) minors, for networks requiring F3, F4, F5 and Fq, respectively. We finally prove that network coding can make a difference from routing only if the network contains a K4 minor, and this minor containment result is tight. Practical implications of the above results are discussed.

Multimedia services including IPTV require huge multimedia data transmission on the Internet. In order to improve a throughput of data transmission, network coding has been proposed to use network bandwidth (=throughput) efficiently with error free channel assumption. However, when the channel is not error free, network coding may not increase the throughput. In this case, effective erasure recovery codes such as Raptor codes have to be used with the network coding. We present the advantage of Raptor codes combined with network coding for high throughput multimedia data transmission services like IPTV. For the applications allowing retransmission, hybrid-ARQ combined with network coding is also considered.

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.

Realistic network environments are commonly emulated by Internet application developers to test both the performance and the correctness of their applications. In this paper, we argue that emulating just realistic network environments may be inadequate for detecting hard-to-detect faults that have very low occurrence probabilities but potentially high impact if exposed in the real world. Specifically, we conduct extensive experiments to study the correctness testing capabilities of realistic and unlikely network environments. Our results show that small investments in emulating unlikely network environments may help in quickly detecting otherwise hard-to-detect faults.

We introduce an efficient way of performing polynomial multiplication in a class of finite fields GF(pm) in the frequency domain. The Fast Fourier Transform (FFT) based frequency domain multiplication technique, originally proposed for integer multiplication, provides an extremely efficient method for multiplication with the best known asymptotic complexity, i.e. O(n log n log log n). Unfortunately, the original FFT method bears significant overhead due to the conversions between the time and the frequency domains, which makes it impractical to perform multiplication of relatively short (160 - 1024 bits) integer operands as used in many applications. In this work, we introduce an efficient way of performing polynomial multiplication in finite fields using the FFT. We show that, with careful selection of parameters, all the multiplications required for the FFT computations can be avoided and polynomial multiplication in finite fields can be achieved with only O(m) multiplications in addition to O(m log m) simple shift, addition and subtraction operations. We show that, especially in constrained devices where multiplication is expensive, polynomial multiplication in the suggested finite fields using the FFT outperforms both the schoolbook and Karatsuba methods for practically small finite fields, e.g., relevant to elliptic curve cryptography.

In this paper we are interested in improving the performance of constructive network coding schemes for video transmission over packet lossy networks. A novel unequal packet loss protection scheme R2NC based on low-triangular global coding matrix with ladder-shaped partition will be presented, which combines redundant and random network coding for robust H.264/SVC video transmission. Firstly, the error-correcting capabilities of redundant network coding make our scheme resilient to loss. Secondly, the implementation of random network coding at the intermediate nodes with multiple input links can reduce the cost of network bandwidth, thus reducing the end to end delay for video transmission. Thirdly, the low-triangular global coding matrix with ladder-shaped partition is maintained throughout R2NC process to provide unequal erasure protection for H.264/SVC priority layers. The redundant network coding avoids the retransmission of lost packets and improves error correcting capabilities of lost packets. Based only on the knowledge of the loss rates on the output links, the source node and intermediate nodes can make decisions for redundant network coding and random network coding (i.e., how much redundancy to add at this node). However, the redundancy caused by redundant network coding makes the network load increases, in order to improve network throughput, we perform random network coding at the intermediate nodes. Our approach is grounded on the overall distortion of reconstructed video minimization by optimizing the amount of redundancy assigned to each layer. Experimental results are shown to demonstrate the significant improvement of H.264/SVC video reconstruction quality with R2NC over packet lossy networks.

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

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.

SummaryIn the past few years, many publish/subscribe‐based information‐centric network (PS‐ICN) architectures have been proposed and investigated to efficiently deliver information from content publishers to subscribers. However, most existing studies on PS‐ICN have not considered how to utilize in‐network caches, which is a common but important feature in ICN. To address this issue, in this paper, we propose a novel cache‐aware K‐anycast routing scheme, namely, CAKA, that can significantly improve the performance of content delivery. Specifically, we choose PURSUIT, which is one of the most important PS‐ICN architectures, and leverage its bidirectional communication procedure to do the following: (1) enable multiple publishers to send probing messages to the same subscriber; and (2) allow the subscriber to retrievecontent objectsusingK‐anycast routingandnetwork coding. In this study, we extend the PURSUIT protocol to support cache‐aware K‐anycast routing and design the algorithms to choose multiple partially disjointed paths for probing, and to select paths for content retrieval. To evaluate the performance of the proposed scheme, we develop not only a simulation testbed, but also a prototype running in a realistic network environment. Our studies show that the proposed scheme can significantly reduce the average hops to retrieve content objects, with very small overheads. Copyright © 2015 John Wiley & Sons, Ltd.

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.