GRAND-Assisted Random Linear Network Coding in Wireless Broadcasts

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.

Codes in the projective space and codes in the Grassmannian over a finite field-referred to as subspace codes and constant-dimension codes (CDCs), respectively-have been proposed for error control in random linear network coding. For subspace codes and CDCs, a subspace metric was introduced to correct both errors and erasures, and an injection metric was proposed to correct adversarial errors. In this paper, we investigate the packing and covering properties of subspace codes with both metrics. We first determine some fundamental geometric properties of the projective space with both metrics. Using these properties, we then derive bounds on the cardinalities of packing and covering subspace codes, and determine the asymptotic rates of optimal packing and optimal covering subspace codes with both metrics. Our results not only provide guiding principles for the code design for error control in random linear network coding, but also illustrate the difference between the two metrics from a geometric perspective. In particular, our results show that optimal packing CDCs are optimal packing subspace codes up to a scalar for both metrics if and only if their dimension is half of their length (up to rounding). In this case, CDCs suffer from only limited rate loss as opposed to subspace codes with the same minimum distance. We also show that optimal covering CDCs can be used to construct asymptotically optimal covering subspace codes with the injection metric only.

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 with ladder-shaped global coding matrix for robust video transmission

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.

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.

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.

Quadratic permutation polynomial (QPP) has good coding characteristics and parallel processing ability. Random linear network coding (RLNC) is an improved coding algorithm for wireless channel video streaming, which can improve the network throughput and network lifetime of mobile ad hoc network (MANET). In this paper, we study the characteristics of quadratic permutation polynomials (QPP) and RLNC by increasing the amount of available data to the users through the encode nodes. The paper proposes a quadratic permutation polynomials enhancement of a RLNC approach $\mathrm{in}$ MANETs (QPP-RLNC). QPP-RLNC algorithm can better control the complexity of encoding/decoding and restore the original data. The performance of QPP-RLNC algorithm, such as coding overhead, decoding delay, packet loss probability and network throughput, was experimentally studied by using network simulation (NS2) software. Simulation results show that the proposed QPP-RLNC algorithm can improve coding efficiency and 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 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.

To efficiently exploit the broadcast feature of wireless channels, a opportunistic routing protocol based on random linear network coding is proposed for wireless sensor networks. The protocol requires each node except for destination in network to transmit the random linear combination created by all packets in buffer, and confirms the expected number of transmissions according to node’s credit value which is computed by a heuristic algorithm. This approach can overcome the shortcomings of instability of wireless channel quality, and use long and unreliable radio links which would not be used by traditional protocols. The experiment results show that the proposed protocol presents significant performance improvements, especially in network throughput and end-to-end delay.

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.

Scheduling based on random linear network coding is an effective way of improving system performance in a wireless network. In a time-varying channel environment, it is important to take the effects of outdated channel-state information (CSI) into consideration when scheduling because the CSI used may be different from the real CSI for data transmissions due to mobility and feedback delays. Here, we analyze the outage probability for scheduling based on random linear network coding in an outdated CSI environment. Practical scenarios are assessed so that the outage probability performance can be evaluated reliably.

Tactile Internet (TI) has very stringent networking requirements and the transport layer plays a crucial role in meeting these requirements. However, the transport layer has several inherent limitations (e.g., bufferbloat, incast issue, and head of line blocking) due to which the performance of the current transport layer solutions is not optimal. We advocate replacing the "store-and-forward" strategy in transport layer solutions with the "compute-and-forward" strategy. One way to implement the "compute-and-forward" strategy is random linear network coding (RLNC). This paper proposes a learning-based RLNC framework called RS-RLNC that utilizes network and receiver feedback to optimally select between block-RLNC and sliding-RLNC to improve overall network performance. We present a simulation-based performance evaluation of current transport layer solutions against the state-of-the-art RLNC and RS-RLNC in terms of throughput, latency, and decoding complexity. Delay is reduced by a factor of 8.5% and decoding complexity is improved up to 20% compared to the state-of-the-art. Simulation results indicate that RS-RLNC has the potential to meet the stringent requirements of TI applications. Additionally, we present three future directions outlining the evolution of RS-RLNC to enhance the transport layer for TI compatibility.

SummaryIn Delay Tolerant Networks (DTNs), mobile nodes exploit encounter chances to transmit data via the established opportunistic link between encounter nodes. The transmission capacity between two encounter nodes is constrained by the duration of opportunistic links. How to transmit data efficiently is one of the fundamental and most important issues in DTNs. Recently, Random Linear Network Coding (RLNC) is proposed as a promising approach to improve data transmission efficiency in DTNs. To facilitate the development of deployment of RLNC based routing protocols, it is imperative to quantify the performance gain brought by RLNC in a rigorous and systematic way. In this paper, we develop an analytical model to evaluate the data transmission performance of RLNC based epidemic routing in DTNs. In the model, we consider that multiple unicast communication sessions compete for limited \capacity. Numerical results validate the effectiveness of our analytical model and demonstrate the significant performance improvement for data transmission in DTNs brought by RLNC. Our work of this paper provides a general tool for performance evaluation and useful guidelines for designing RLNC based routing protocols in DTNs. Copyright © 2015 John Wiley & Sons, Ltd.