Random linear network coding with ladder-shaped global coding matrix for robust video transmission

The network coding capacity of a single multicast traffic is characterized by the min-cut/max-flow (mcMF) theorem, which can be achieved by random linear network coding (RLNC). Nonetheless, the graph-theoretic characterization for multiple unicast/multicast traffic remains an open problem. This paper proposes and studies a new class of intersession-network-coding schemes: RLNC with selective cancelling (SC), which inherits the complexity advantage of RLNC once the set of selective cancelling edges is decided. A graph-theoretic characterization is provided for the achievable rates of RLNC with SC for the general multiple multicast setting. The findings contain most existing achievability results as special cases, including the mcMF theorem of the single multicast traffic and the existing characterization of pairwise intersession network coding. One prominent feature of the proposed approach is its focus on the achievability analysis with arbitrary network topology, arbitrary inter-session packet-mixing capability, and arbitrary traffic demands, which distinguishes the results from the special case analysis, capacity outer bound constructions, and the pattern-based (butterfly-based) superposition arguments.

Random linear network coding (RLNC) has the potential to improve the performance of current and future Internet of Things (IoT) communication systems, but is computationally demanding due to matrix multiplications and inversions. Some single-core RLNC implementations achieve already sufficient coding speeds for contemporary multimedia streaming formats. However, advances in multimedia streaming formats and IoT applications will require the exploitation of heterogeneous multicore architectures, which are becoming common for a wide range of IoT nodes, including smartphones. In this paper, we introduce and evaluate efficient RLNC computing strategies for IoT node architectures, including the emerging heterogeneous big.LITTLE multicore architectures with multiple big (fast) cores and multiple LITTLE (slow) cores. In contrast to existing RLNC implementation strategies, we build on and adapt highly optimized dense matrix operations from the high performance computing field to RLNC on heterogeneous multicore IoT nodes. Our approach includes the optimization of RLNC matrix operations through optimized operations on matrix blocks with single instruction multiple data instructions. We schedule block operations on the heterogeneous cores through a directed acyclic graph that avoids artificial synchronization points while ensuring the data dependencies. We examine priority scheduling according to the number of outgoing dependencies of a task and data locality of cached blocks. Our extensive measurements with several heterogeneous big.LITTLE multicore IoT node and smartphone processor boards demonstrate higher RLNC encoding and decoding throughputs than existing approaches. Moreover, our measurements indicate that the utilization of more cores decreases energy consumption, which is an important goal for IoT nodes.

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.

Passive network tomography uses end-to-end observations of network communication to characterize the network, for instance to estimate the network topology and to localize random or adversarial glitches. Under the setting of linear network coding this work provides a comprehensive study of passive network tomography in the presence of network (random or adversarial) glitches. To be concrete, this work is developed along two directions: 1. Tomographic upper and lower bounds (i.e., the most adverse conditions in each problem setting under which network tomography is possible, and corresponding schemes (computationally efficient, if possible) that achieve this performance) are presented for random linear network coding (RLNC). We consider RLNC designed with common randomness, i.e., the receiver knows the random code-books all nodes. (To justify this, we show an upper bound for the problem of topology estimation in networks using RLNC without common randomness.) In this setting we present the first set of algorithms that characterize the network topology exactly. Our algorithm for topology estimation with random network errors has time complexity that is polynomial in network parameters. For the problem of network error localization given the topology information, we present the first computationally tractable algorithm to localize random errors, and prove it is computationally intractable to localize adversarial errors. 2. New network coding schemes are designed that improve the tomographic performance of RLNC while maintaining the desirable low-complexity, throughput-optimal, distributed linear network coding properties of RLNC. In particular, we design network codes based on Reed-Solomon codes so that a maximal number of adversarial errors can be localized in a computationally efficient manner even without the information of network topology.

Network error localizations uses end-to-end observations to localize random or adversarial glitches. For error localization under random linear network codes (RLNCs) the schemes proposed in previous literatures require the priori knowledge of the network topology. Moreover, adversarial error localization is proved computationally intractable under RLNCs. The goal of current paper is designing new network coding schemes to improve the error localization performance of RLNCs while maintaining the key advantages of RLNCs. To be concrete, we introduce Network Reed-Solomon codes (NRSCs), which have the following features: 1. NRSCs are low-complexity distributed linear network codes. 2. NRSCs achieve the network multicast capacity with high probability. 3. In adversarially faulty networks NRSCs enable the receiver to locate a maximum number of adversarial errors in a computationally efficient manner. Moreover, the error localization schemes under NRSCs do not need the priori knowledge of the network topology and thus are robust against dynamic network updating.

In a network application, channel coding alone is not sufficient to reliably transmit a message of finite length K from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. In this scenario RLNC has been shown to have a throughput advantage over TDMA schemes as K→∞ and q→∞. In this paper we focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel code rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small message lengths K and small q.

In the study of packet-level random linear network coding (RLNC) in wireless broadcast, RLNC over GF(2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^L</i>) is known to asymptotically achieve the optimal completion delay with increasing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i>. Effective utilization of guessing random additive noise decoding (GRAND) at the physical layer can help leverage RLNC packets to generate syndromes so as to reduce packet erasure probabilities and thus further improve the completion delay performance. Prior to this work, only a few studies investigated GRAND-assisted RLNC and they restricted to GF(2)-coding. In this paper, we first provide a general framework to formulate the decoding process of GRAND-assisted RLNC over GF(2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^L</i>) for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ≥ 1. Even for GRAND-assisted GF(2)-RLNC, the formulation is more complete than previous considerations in the sense that it takes the a priori information of which packets have errors into consideration. Moreover, we propose a novel GRAND-assisted GF(2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^L</i>)-RLNC scheme whose computational overhead introduced by GRAND is negligible. In particular, a subset of GF(2<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">^L</i>) is carefully designed for random coding coefficient selection. For the novel scheme, we theoretically derive lower bounds on the distribution as well as an upper bound on the expected value of the completion delay. Numerical results demonstrate not only a reduction in average completion delay for the novel scheme, but also the advantage of random coding coefficient selection from the specially designed subset for GRAND-assisted RLNC schemes.

ERSS-RLNC: Efficient and robust secure scheme for random linear network coding

Wireless networks typically employ some form of forward error correction (FEC) coding and some automatic repeat request (ARQ) protocol to ensure reliable data transmission over lossy channels. We propose to integrate FEC and ARQ in the context of random linear network coding (RLNC). In particular, we develop Caterpillar RLNC with feedback (CRLNC-FB), an RLNC approach with a finite sliding packet transmission window in conjunction with feedback-based selective repeat ARQ. CRLNC-FB employs a novel RLNC decoding method based on a band-form of Gaussian elimination. In response to lost packets, CRLNC-FB retransmits lost packets in systematic (uncoded) form to aid fast in-order packet delivery at the receiver. Extensive performance evaluations indicate that CRLNC-FB gives higher throughput-delay performance than the preceding RLNC approaches with feedback. In particular, CRLNC-FB with its sliding window achieves lower delays than block-based RLNC. Also, the retransmission of uncoded source packets in CRLNC-FB contributes to a significantly higher throughput-delay performance than loss recovery through coded packets interspersed among future source packets at a prescribed code rate.

he usage of random linear network coding in wireless sensor network is consistent with sociality, for this feature, proposed a network coding scheme for sociality for wireless sensor networks. Analyzed the process of coding and decoding of random linear network coding and summarized the advantages and disadvantages of the scheme in practical application, at last through NS2 to compare the scheme of using random linear network coding and traditional coding, the random linear network is better at network performance.

This paper addresses the issue of throughput-delay of one-to-many wireless multi-hop flows based on random linear network coding (RLNC). Existing research results have been focusing on the single-hop model which is not suitable for wireless multi-hop networks. In addition, the conditions of related system model are too idealistic. To address these limitations, we herein investigate the performance of a wireless multi-hop network, focusing on the one-to-many flows. Firstly, a system model with multi-hop delay was constructed; secondly, the transmission schemes of system model were gradually improved in terms of practical conditions such as limited queue length and asynchronous forwarding way; thirdly, the mean delay and the mean throughput were quantified in terms of coding window size if and number of destination nodes N for the wireless multi-hop transmission. Our findings show a clear relationship between the multi-hop transmission performance and the network coding parameters. This study results will contribute significantly to the evaluation and the optimization of network coding method.

In order to improve the throughput and transmission reliability in wireless sensor network with limited resources, multicast network coding technology is imported in. On this basis, through random linear network coding by nodes' cooperation to make improvement in delayed and expense. The simulation results show that the transmission, to the opportunity routing, by cooperation network coding strategies is improved in making full use of space-time reusability, reducing the delay and enhancing the throughput and transmission reliability of wireless sensor network.

A typical intelligent factory, a smart home or a smart city consists of several nodes or machines. In a typical Machine to Machine Communication mode (M2M), each machine senses some information (pressure, temperature, presence of person, etc.) and then communicates this information to other machines. This communication could be unicast or multicast depending on the application. Further, the destination node of the M2M communication is many-a-times not in the direct communication range. In the presence of tens and hundreds of machines forming a network, it is essential to have an efficient communication mechanism for multihop multicast transmission between different machines. This paper proposes a network coding (NC) based multihop multicast communication for different topologies - butterfly, flattened butterfly, hypercube and folded-clos model. It is observed that random linear network coding (RLNC) technique outperforms best routing protocol for different topologies, by requiring less time for data transmission, reducing the time required by upto 50%, depending on the model. Further, in order to improve the performance of network coding for M2M in a disconnected network; an integrated network coding and routing approach is proposed and evaluated. It is observed that such an integrated mechanism requires upto 25% less time than pure routing and upto 10% less time than required by RLNC.

A fundamental understanding of the relationship between delay performance and complexity in network coding is instrumental towards its application in practical systems. The main argument against delay-optimal random linear network coding (RLNC) is its decoding complexity, which is O(n 3 ) for n original packets. Fountain codes, such as LT and Raptor codes, reduce the decoding load on the receiver but at the cost of introducing additional, non-negligible delay. The source of this increased delay is the inherent sparsity of the code, which significantly reduces the impact of a new coded packet, i.e., the probability of a packet to be linearly independent from the knowledge at the receiver, as we approach the end of the transmission (when few degrees of freedom are missing). Thus, the additional overhead is mainly due to the transmission of the last data packets. Our key observation is that switching gears to denser codes as the transmission process progresses could considerably reduce the delay overhead while maintaining the complexity advantages of a sparse code. We propose tunable sparse network coding as a dynamic coding mechanism with a code structure with two regions: a sparse region, with various levels of sparsity, and a dense region, where packets are generated as per RLNC. We characterize the problem in multicast sessions on general networks and illustrate trade-offs in especial cases of interest. We also present a novel mechanism to perform efficient Gaussian elimination for sparse matrices that guarantees linear decoding complexity with high probability.

Network coding is a promising technology which allows coding of multiple packets in routers. Random linear network coding (RLNC), a distributed network coding scheme, insists each node to forward independent random linear combinations of incoming packets through its outgoing links. RLNC appends a header which contains the information about how the linear combinations are taken. We observe that some additional flexibility can be induced in RLNC header with minor modification in decoding. Our modification does not make any increase in computational complexity. We also demonstrate some applications of it in secure network coding and error correction.