Network Coding Research Articles

On Lattice Network Coding Based Cell-Free MIMO With Uncoordinated Base Stations

On Lattice Network Coding Based Cell-Free MIMO With Uncoordinated Base Stations

SC-PNC: Semantic Communication-Empowered Physical-Layer Network Coding

SC-PNC: Semantic Communication-Empowered Physical-Layer Network Coding

On parallelisms of PG(3,4) with automorphisms of order 2

Let PG(n,q) be the n-dimensional projective space over the finite field Fq. A spread in PG(n,q) is a set of mutually skew lines which partition the point set. A parallelism is a partition of the set of lines by spreads. The classification of parallelisms in small finite projective spaces is of interest for problems from projective geometry, design theory, network coding, error-correcting codes, and cryptography. All parallelisms of PG(3,2) and PG(3,3) are known. Parallelisms of PG(3,4) which are invariant under automorphisms of odd prime orders have also been classified. The present paper contributes to the classification of parallelisms in PG(3,4) with automorphisms of even order. We focus on cyclic groups of order four and the group of order two generated by a Baer involution. We examine invariants of the parallelisms such as the full automorphism group, the type of spreads and questions of duality. The results given in this paper show that the number of parallelisms of PG(3,4) is at least 8675365. Some future directions of research are outlined.

Simultaneous update of sensing and control data using free-ride codes in vehicular networks: An age and energy perspective

In real-time Internet of Things networks, age of information (AoI) and energy cost (EC) are generally deemed as two significant performance metrics to characterize the information freshness and energy efficiency. This paper aims at updating not just sensing data but sensing data and control data simultaneously in vehicular networks. By employing the promising free-ride coding mechanism, the randomly encoded control data is superposed on the low-density parity-check coded sensing data and then is sent to the receiver, consuming neither additional bandwidth nor transmission power. Considering the time and energy of both status update generation and transmission, the average AoI (AAoI) and average EC (AEC) expressions are derived for preemptive and blocking updating schemes with truncated automatic repeat request protocol. Numerical simulations present the AAoI of both sensing data and control data, as well as the AEC of the transmitter, which demonstrate that free-ride coding mechanism not only can improve the freshness of control data but impose an insignificant influence on the performance of sensing data. Moreover, comparison with the blocking scheme suggests that the preemptive one obtains the smaller AAoI but the larger AEC.

Temporal resolution of spike coding in feedforward networks with signal convergence and divergence.

Convergent and divergent structures in the networks that make up biological brains are found universally across many species and brain regions at various scales. Neurons in these networks fire action potentials, or "spikes", whose precise timing is becoming increasingly appreciated as large sources of information about both sensory input and motor output. While previous theories on coding in convergent and divergent networks have largely neglected the role of precise spike timing, our model and analyses place this aspect at the forefront. For a suite of stimuli with different timescales, we demonstrate that structural bottlenecks (small groups of neurons) post-synaptic to network convergence have a stronger preference for spike timing codes than expansion layers created by structural divergence. Additionally, we found that a simple network model with similar convergence and divergence ratios to those found experimentally can reproduce the relative contribution of spike timing information about motor output in the hawkmoth Manduca sexta. Our simulations and analyses suggest a relationship between the level of convergent/divergent structure present in a feedforward network and the loss of stimulus information encoded by its population spike trains as their temporal resolution decreases, which could be confirmed experimentally across diverse neural systems in future studies. We further show that this relationship can be generalized across different models and measures, implying a potentially fundamental link between network structure and coding strategy using spikes.

Leveraging Linear Network Error Correction for steganographic network codes

Steganography is an ingenious method employed to conceal data within an unassuming, non-secret file or message, thereby evading detection. The concealed information is later extracted at its intended destination. Many legitimate applications of steganography exist, ranging from hiding watermarks or trademarks covertly within multimedia or other content files, to embedding sensitive information securely. In this paper, we introduce Steganographic schemes employing Linear Network Error Correction Codes (LNECCs). Initially, we emphasize the enhanced throughput achieved through the integration of steganography into joint channel-network codes, then we demonstrate the feasibility of leveraging LNECCs and their corresponding error patterns to formulate distortion-free steganographic schemes. Specifically, for a given LNECC in relation to a terminal and a resolvable error pattern, with the precondition that the minimum cut between them is positive, we delineate the corresponding distortion-free steganographic protocols. Moreover, we conduct a thorough analysis of our scheme and fortify it against potent steganalysis attacks. Finally, we propose a prospective solution for cases involving erroneous retrievals.

Asymptotically optimal [2k+1,k,k]q-almost affinely disjoint subspaces

Let Fq denote the finite field of size q and Fqn denote the set of n-tuples of elements from Fq. A family of k-dimensional subspaces of Fqn, which forms a partial spread, is called L-almost affinely disjoint (or briefly [n,k,L]q-AAD) if each affine coset of a member of this family intersects with only at most L subspaces from the family.Polyanskii and Vorobyev introduced AAD subspace families in [23] (2019) in order to construct some types of primitive batch codes. For this purpose, they made use of Reed-Solomon codes and hence they presented [n=2k+1,k,L=k]-AAD subspace families of size ⌊q/k⌋. Later on, AAD spaces received a notable attention and have been studied for various parameters, see Liu et al. [18] (2021) and Otal and Arıkan [21] (2022) for example.In Arıkan et al. (2023) [1], we presented a construction of [2k+1,k,k]-AAD subspace families of size q, which improves the lower bound ⌊q/k⌋ given by Polyanskii and Vorobyev in [23] (2019) k times. We also proved that our construction yields AAD subspace families for k=2 and k=3, and left the proof of the case k≥4 as a conjecture.In this paper, we now prove this conjecture by a newer and more abstract approach. For the proof, we carefully utilize several sophisticated arguments coming from coding theory, algebraic geometry, and linear algebra. In particular, we interpret each subspace as a suitable generator matrix (the lifting idea in random network coding), then algebraically manipulate their AAD-ness relation and produce suitable Van der Monde matrices (the fundamental tools for the BCH bound in coding theory), later apply Cramer's rule (a well-known key tool in linear algebra), and lastly obtain low-degree polynomials as contradictions (the trick coming from algebraic geometry utilized for Goppa codes). We present our constructive proof step-by-step to make it more easy to understand.

RL-ANC: Reinforcement Learning-Based Adaptive Network Coding in the Ocean Mobile Internet of Things

As the demand for sensing and monitoring the marine environment increases, the Ocean Mobile Internet of Things (OM-IoT) has gradually attracted the interest of researchers. However, the unreliability of communication links represents a significant challenge to data transmission in the OM-IoT, given the complex and dynamic nature of the marine environment, the mobility of nodes, and other factors. Consequently, it is necessary to enhance the reliability of underwater data transmission. To address this issue, this paper proposes a reinforcement learning-based adaptive network coding (RL-ANC) approach. Firstly, the channel conditions are estimated based on the reception acknowledgment, and a feedback-independent decoding state estimation method is proposed. Secondly, the sliding coding window is dynamically adjusted based on the estimates of the channel erasure probability and decoding probability, and the sliding rule is adaptively determined using a reinforcement learning algorithm and an enhanced greedy strategy. Subsequently, an adaptive optimization method for coding coefficients based on reinforcement learning is proposed to enhance the reliability of the underwater data transmission and underwater network coding while reducing the redundancy in the coding. Finally, the sampling period and time slot table are updated using the enhanced simulated annealing algorithm to optimize the accuracy and timeliness of the channel estimation. Simulation experiments demonstrate that the proposed method effectively enhances the data transmission reliability in unreliable communication links, improves the performance of underwater network coding in terms of the packet delivery rate, retransmission, and redundancy transmission ratios, and accelerates the convergence speed of the decoding probability.

External codes for multiple unicast networks via interference alignment.

We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a finite field. In this context, we establish an outer bound for the achievable rate region and provide examples of networks where the bound is sharp. We finally give evidence of the crucial role played by the field characteristic in the problem.

Flexible Quantum Network Coding by Using Quantum Multiplexing

AbstractQuantum network coding (QNC) aims at alleviating quantum communication congestion in quantum networks. Although several QNC protocols have been presented, they cannot meet the practical requirements that part of source nodes intend to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously. Here, the study presents a flexible QNC protocol by using quantum multiplexing. First, the entangled pairs are generated between adjacent nodes in a heralded way by using quantum multiplexing. Then the quantum memories of the source nodes and the ones of the corresponding target nodes are entangled when the intermediate nodes execute multiple rounds of entanglement swapping operations on their quantum memories. Finally, the quantum states are transmitted from the source nodes to their corresponding target nodes by means of quantum teleportation. Compared with the existing protocols, the protocol allows an arbitrary part of the source nodes to transmit their quantum states with same or different qubit numbers via the bottleneck network simultaneously, thereby exhibiting its flexibility.

Network Coding with Parallel Path Protection for Multiple Link Failure in WOBAN

Background: WOBAN is a high-speed network and hence any kind of failure results in huge data loss. Using the proposed network coding technique with parallel path protection can handle multiple link failures, the performance of the network can be improved. Aims: This study aims to improve network performance using network coding with parallel path protection routing algorithm (NC-PPR) for multiple link failures in WOBAN. Objective: We investigated the multiple link failures in WOBAN by the proposed approach namely Coded Path Protection Algorithm, which enhances the survivability of the WOBAN against multiple link failures in the front end and eliminates the need of backup resources. Methods: Extensive simulation is carried out to implement proposed work. A simulation model and code is developed in MATLAB to get the performance enhancement of WOBAN. Results: We compared the performance of proposed algorithm with existing algorithm. The obtained results show that the proposed algorithm has superior performance than the existing algorithm. Conclusion: In this paper, a new routing approach, which works in three phases namely path finding, encoding, and decoding, using random linear network coding (RLNC) is introduced to address the survivability issue of the WOBAN. The proposed approach also enhances the network performance in terms of PDR, overhead, and delay.

A Network Coding Scheme Transmitting Specific Data and Universal Data Based on Deep Learning

A Network Coding Scheme Transmitting Specific Data and Universal Data Based on Deep Learning

Maximum flag-rank distance codes

In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding. In this setting we provide a Singleton-like bound which relates the parameters of a flag-rank-metric code. This allows us to introduce the family of maximum flag-rank distance codes, that are flag-rank-metric codes meeting the Singleton-like bound with equality. Finally, we provide several constructions of maximum flag-rank distance codes.

A Certificateless Linearly Homomorphic Signature Scheme Based on Lattice for Network Coding

Abstract Homomorphic signature is an extremely important public key authentication technique for network coding to defend against pollution attacks. However, there are many problems with previous homomorphic signature schemes which require key escrow, cannot resist malicious key generation center (KGC), and are insecure in the post-quantum era. Therefore, we propose a lattice-based certificateless linearly homomorphic signature scheme. In our scheme, certificateless structure can avoid key escrow and malicious KGC. The lattice structure ensures that our scheme is secure in the post-quantum era. The bimodal Gaussian distribution is used to improve the security and the efficiency. Compared with the previous schemes, our scheme has smaller storage space (no key escrow), can avoid malicious KGC, is more secure in the post-quantum era, and has higher signature efficiency. At the same time, our scheme is more suitable for network coding. Finally, under random oracle model, we proved that our scheme is weakly context hiding and existentially unforgeable against adaptive chosen message attacks against external attackers and the internal KGC.

The artificial neural network approach for the transmission of malicious codes in wireless sensor networks with Caputo derivative

AbstractThe current manuscript investigates a six compartmental mathematical model for malicious Codes in Wireless Sensor Network is consider for investigation under the fractional operator of Caputo along with their numerical scheme. The six agent nodes of the network sensors are transferable like in infection with in their community of different nodes. With the help of fixed point theory the presentation of existence and uniqueness of solution of the said model are also given. The scheme of numerical solution under fractional format is developed with the choice of fractional orders which increasing the degree of freedom for such type of network analysis. The numerical simulation of all the six agents are given on different fractional orders along with sensitivity of the fractional orders and some used parameters. The new analysis artificial neural network (ANN) method has been utilized for the considered model and compared with Adams–Bashforth (AB) method. We divided the data set into three categories training, testing and validation with ANN method and the analysis is presented in this work.

AQUA: Analytics-driven quantum neural network (QNN) user assistance for software validation

This paper proposes a novel analytics-driven user assistance software validation approach for quantum neural network (QNN) codes. The proposed analytics-driven QNN user assistance (AQUA) for software validation considers user interactive feedback for constructing efficient QNN software. Our proposed AQUA is based on dynamic software testing and analysis due to undetermined qubit states in QNN which is hard to be tracked via static software analysis. AQUA is for plotting gradient variances to determine whether the QNN software suffers from local minima situations, which are called barren plateaus in QNN. By utilizing AQUA software validation, the stability, feasibility, and explainability of QNN software can be tested. AQUA has been tested using real-world case study with quantum convolutional neural network software for point cloud data processing in autonomous driving applications.

Adjustable random linear network coding (ARLNC): a solution for data transmission in dynamic IoT computational environments

In mobile computing environments, most IoT devices connected to networks experience variable error rates and possess limited bandwidth. The conventional method of retransmitting lost information during transmission, commonly used in data transmission protocols, increases transmission delay and consumes excessive bandwidth. To overcome this issue, forward error correction techniques, e.g., Random Linear Network Coding (RLNC) can be used in data transmission. The primary challenge in RLNC-based methodologies is sustaining a consistent coding ratio during data transmission, leading to notable bandwidth usage and transmission delay in dynamic network conditions. Therefore, this study proposes a new block-based RLNC strategy known as Adjustable RLNC (ARLNC), which dynamically adjusts the coding ratio and transmission window during runtime based on the estimated network error rate calculated via receiver feedback. The calculations in this approach are performed using a Galois field with the order of 256. Furthermore, we assessed ARLNC's performance by subjecting it to various error models such as Gilbert Elliott, exponential, and constant rates and compared it with the standard RLNC. The results show that dynamically adjusting the coding ratio and transmission window size based on network conditions significantly enhances network throughput and reduces total transmission delay in most scenarios. In contrast to the conventional RLNC method employing a fixed coding ratio, the presented approach has demonstrated significant enhancements, resulting in a 73% decrease in transmission delay and a 4 times augmentation in throughput. However, in dynamic computational environments, ARLNC generally incurs higher computational costs than the standard RLNC but excels in high-performance networks.

On Achievable Rates of Line Networks With Generalized Batched Network Coding

On Achievable Rates of Line Networks With Generalized Batched Network Coding

SECURE CLOUD STORAGE PROTOCOL WITH DATA DYNAMICS USING DSCS PROTOCOL

The goal of the project "Secure Cloud Storage Protocol With Data Dynamics Using DSCS Protocol" is to create a cutting-edge cloud storage protocol that cleverly integrates network coding technologies to combine efficiency and security. The goal of this project is to provide strong protection against data loss and illegal access while improving the performance and dependability of cloud storage systems. The suggested protocol distributes and encrypts data among several cloud network nodes using network coding techniques. This strengthens the system against possible data loss or corruption by introducing redundancy and error correction in addition to optimizing data transit and storage efficiency. Key Words: cloud, private key, sensitive data, Network Coding

Fast decoding of lifted interleaved linearized Reed–Solomon codes for multishot network coding

Martínez-Peñas and Kschischang (IEEE Trans. Inf. Theory 65(8):4785–4803, 2019) proposed lifted linearized Reed–Solomon codes as suitable codes for error control in multishot network coding. We show how to construct and decode lifted interleaved linearized Reed–Solomon (LILRS) codes. Compared to the construction by Martínez-Peñas–Kschischang, interleaving allows to increase the decoding region significantly and decreases the overhead due to the lifting (i.e., increases the code rate), at the cost of an increased packet size. We propose two decoding schemes for LILRS that are both capable of correcting insertions and deletions beyond half the minimum distance of the code by either allowing a list or a small decoding failure probability. We propose a probabilistic unique Loidreau–Overbeck-like decoder for LILRS codes and an efficient interpolation-based decoding scheme that can be either used as a list decoder (with exponential worst-case list size) or as a probabilistic unique decoder. We derive upper bounds on the decoding failure probability of the probabilistic-unique decoders which show that the decoding failure probability is very small for most channel realizations up to the maximal decoding radius. The tightness of the bounds is verified by Monte Carlo simulations.