Network Error Correction Coding Research Articles

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.

A Revisit of Linear Network Error Correction Coding

A Revisit of Linear Network Error Correction Coding

A Discrete Polymatroidal Framework for Differential Error-Correcting Index Codes

In the conventional index coding problem, the messages transmitted by the source to satisfy the demands of the receivers are error-free. However, in practice, the messages may be error prone which led to the introduction of error-correcting index codes. An error-correcting index code is an encoding scheme which enables every receiver to decode its demanded message even in the presence of certain number of transmission errors. Formally, an index code capable of correcting at most $\delta $ errors at all its receivers is defined as a $\delta $ -error-correcting index code. In this paper, we explore the connections between vector linear error-correcting index codes and discrete polymatroids. This is motivated from the connections between linear network error-correcting codes and matroids. It is shown that a vector linear error-correcting index code exists if and only if there exists a representable discrete polymatroid satisfying certain conditions. Differential error-correcting index codes which allow different receivers to have different error-correcting capabilities are also studied. Note that the $\delta $ -error-correcting code is a special case of a differential error-correcting index code. Error correction at a subset of receivers is another special case which is discussed.

Malicious node detection through run time self-healing algorithm in WSN

Wireless sensor network possess a large number of randomly deployed nodes. These nodes configure themselves to form a network. WSNs' major role is to monitor the environment, collect the data and communicate the data to the base node. The originality of the data communicated by the WSN nodes is an important criterion to avoid failure in the network. So, self-healing techniques are implemented to overcome the losses of data in routing due to misbehaving nodes. However, major protocols designed for self-healing are not energy constrained and not suitable for battery powered network. In this paper, we propose a new run-time self-healing algorithm which possesses individual monitoring node capable of scanning the data and evaluate the stability of the nodes to ensure proper communication in the network. The proposed method is compared with self-healing hybrid sensor network architecture (SASHA) and error correction code (ECC) algorithm to validate the proposed system efficiency. The simulation results show that the proposed algorithm improves efficiency by 86%.

On Capacity of Network Error Correction Coding With Random Errors

In this letter, we consider the capacity results of network error correction coding over a general multicast network, where a malicious error occurs on each edge with a fixed probability $p$ at each transmission. A pair of upper and lower bounds on the capacity are given, which are proved to coincide for a unicast network with $|\mathcal {E}|$ parallel channels connected directly from source to sink node, where $\mathcal {E}$ is the edge set of the network. A scheme with non-linear coding at the source and linear coding at the intermediate nodes is proposed, which achieves a strictly higher transmission rate than linear network coding.

Matroidal error correction networks and linear network error correction MDS codes

In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case when errors occur in multiple channels. Importantly, we show the necessary and sufficient conditions on the existence of linear network error correction multicast/ broadcast/dispersion maximum distance separable (MDS) code on a matroidal error correction network.

Construction of Network Error Correction Codes in Packet Networks

Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to NEC, especially the Singleton bound. In this paper, following the research line using the extended global encoding kernels proposed by Zhang in 2008, the refined Singleton bound of NEC can be proved more explicitly. Moreover, we give a constructive proof of the attainability of this bound and indicate that the required field size for the existence of network maximum distance separable (MDS) codes can become smaller further. By this proof, an algorithm is proposed to construct general linear network error correction codes including the linear network error correction MDS codes. Finally, we study the error correction capability of random linear NEC. Motivated partly by the performance analysis of random linear network coding, we evaluate the different failure probabilities defined in this paper in order to analyze the performance of random linear NEC. Several upper bounds on these probabilities are obtained and they show that these probabilities will approach to zero as the size of the base field goes to infinity. Using these upper bounds, we slightly improve on the probability mass function of the minimum distance of random linear network error correction codes in a paper by Balli and colleagues, as well as the upper bound on the field size required for the existence of linear network error correction codes with degradation at most <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> .

Design of Network Codes for Multiple-User Multiple-Relay Wireless Networks

We investigate the design of network codes for multiple-user multiple-relay (MUMR) wireless networks with slow fading (quasi-static) channels. In these networks, M users have independent information to be transmitted to a common base station (BS) with the help of N relays, where M ≥ 2 and N ≥ 1 are arbitrary integers. We investigate such networks in terms of diversity order to measure asymptotic performance. For networks with orthogonal channels, we show that network codes based on maximum distance separable (MDS) codes can achieve the maximum diversity order of N+1. We further show that the MDS coding construction of network codes is also necessary to obtain full diversity for linear finite field network coding (FFNC). Then, we compare the performance of the FFNC approach with superposition coding (SC) at the relays. The results show that the FFNC based on MDS codes has better performance than SC in both the high rate and the high SNR regime. Further, we discuss networks without direct source-to-BS channels for N ≥ M. We show that the proposed FFNC can obtain the diversity order N-M+1, which is equivalent to achieving the Singleton bound for network error-correction codes. Finally, we study the network with nonorthogonal channels and show our codes can still achieve a diversity order of N+1, which cannot be achieved by a scheme based on SC.

Theory and Applications of Network Error Correction Coding

Network error correction coding (NEC) has attracted a lot of attention in recent years because of its potential usefulness in network communications. Several kinds of errors may occur in communication networks using network coding. This includes random errors, erasures, and errors caused by attacks from malicious nodes. The main goal of the theory of NEC is to deal with these errors efficiently. Two kinds of network models have been considered in network coding theory: coherent and noncoherent networks. A network is called coherent if network characteristics are known to senders and receivers, and called noncoherent if they are unknown. Although both scenarios are theoretically interesting, the noncoherent network model fits better to the requirements in most applications. So far, there are two lines of research in the theory of NEC. One approach follows the classical method by representing messages by sequences and the other approach uses the theory of rank metric codes for network error correction by representing messages by subspaces. Following both approaches, basic theories have been developed. This includes the formulation of channel models, the characterization of error correction/detection capabilities for various kinds of errors, the derivation of bounds for NECs, the study of existence and constructions of optimal codes, the development of encoding and decoding techniques, and the design of code suitable for real applications. In this paper, we summarize some important contributions in this research direction.

A Survey of Linear Network Coding and Network Error Correction Code Constructions and Algorithms

Network coding was introduced by Ahlswede et al. in a pioneering work in 2000. This paradigm encompasses coding and retransmission of messages at the intermediate nodes of the network. In contrast with traditional store-and-forward networking, network coding increases the throughput and the robustness of the transmission. Linear network coding is a practical implementation of this new paradigm covered by several research works that include rate characterization, error-protection coding, and construction of codes. Especially determining the coding characteristics has its importance in providing the premise for an efficient transmission. In this paper, we review the recent breakthroughs in linear network coding for acyclic networks with a survey of code constructions literature. Deterministic construction algorithms and randomized procedures are presented for traditional network coding and for network-control network coding.

On Randomized Linear Network Codes and Their Error Correction Capabilities

Randomized linear network code for single source multicast was introduced and analyzed in Ho et al. (IEEE Transactions on Information Theory, October 2006) where the main results are upper bounds for the failure probability of the code. In this paper, these bounds are improved and tightness of the new bounds is studied by analyzing the limiting behavior of the failure probability as the field size goes to infinity. In the linear random coding setting for single source multicast, the minimum distance of the code defined in Zhang, (IEEE Transactions on Information Theory, January 2008) is a random variable taking nonnegative integer values that satisfy the inequality in the Singleton bound recently established in Yeung and Cai (Communications in Information and Systems, 2006) for network error correction codes. We derive a bound on the probability mass function of the minimum distance of the random linear network code based on our improved upper bounds for the failure probability. Codes having the highest possible minimum distance in the Singleton bound are called maximum distance separable (MDS). The bound on the field size required for the existence of MDS codes reported in Zhang, (IEEE Transactions on Information Theory, January 2008) and Matsumoto (arXiv:cs.IT/0610121, Oct. 2006) suggests that such codes exist only when field size is large. Define the degradation of a code as the difference between the highest possible minimum distance in the Singleton bound and the actual minimum distance of the code. The bound for the probability mass function of the minimum distance leads to a bound on the field size required for the existence of network error correction codes with a given maximum degradation. The result shows that allowing minor degradation reduces the field size required dramatically.

Linear Network Error Correction Codes in Packet Networks

In this paper, we study basic properties of linear network error correction codes, their construction and error correction capability for various kinds of errors. Our discussion is restricted to the single-source multicast case. We define the minimum distance of a network error correction code. This plays the same role as it does in classical coding theory. We construct codes that can correct errors up to the full error correction capability specified by Singleton bound for network error correction codes recently established by Cai and Yeung. We propose a decoding principle for network error correction codes, based on which we introduce two decoding algorithms and analyze their performance. We formulate the global kernel error correction problem and characterize the error correction capability of codes for this kind of error.

Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound

We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give estimates on the time complexity and the required symbol size of the proposed algorithm. We also estimate the probability of a random choice of local encoding vectors by all intermediate nodes giving a network error-correcting codes attaining the Singleton bound. We also clarify the relationship between the robust network coding and the network error-correcting codes with known locations of errors.

Analysis of network error correction based on network coding

For network error-correcting codes based on network coding an explicit lower bound on the size of source alphabet is presented. This bound is deduced by a Gilbert–Varshamov greedy algorithm. The difficulty of constructing good error-correcting codes for networks is considered and ways of constructing good codes for small-scale networks are dealt with in detail.