Linear Network Error Correction 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

An LEK-Based Design Algorithm for MDS Linear Network Error Correction Codes on Cyclic Multicast Networks

A linear network (LN) code can be described by either global encoding kernels (GEKs) or local encoding kernels (LEKs). In the literature, the multicast property of an LN code is described using GEKs, so the design algorithms for multicast LN codes employ GEKs to check this property. In this paper, a criterion is developed so that LEKs rather than GEKs can be used to check the multicast maximum distance separable (MDS) property of linear network error correction (LNEC) codes on erroneous networks. Further, it is used to develop a design algorithm for multicast MDS LNEC codes on erroneous cyclic networks. This algorithm is more efficient than the algorithm that uses GEKs when the number of edges is high and the interconnection of these edges is low.

Variable-Rate Linear Network Error Correction MDS Codes

In network communication, the source often transmits messages at several different information rates within a session. How to deal with information transmission and network error correction simultaneously under different rates is introduced in this paper as a variable-rate network error correction problem. Apparently, linear network error correction maximum distance separable (MDS) codes are expected to be used for these different rates guaranteeing the maximal error-correcting capability. For this purpose, designing a linear network error correction MDS code based on the existing results for each information rate is an alternative solution, but it is inefficient due to its high complexity. In order to solve the problem more efficiently, we present the concept of variable-rate linear network error correction MDS codes preserving local encoding kernels, that is, these linear network error correction MDS codes of different rates have the same local encoding kernel at each internal node. Thus, each nonsource node always uses the same local kernel for coding, no matter what the rate is. Furthermore, we propose an approach to construct such a family of variable-rate network MDS codes and give an algorithm for efficient implementation. This approach economizes the storage space for each internal node, and saves resources and time for transmissions on networks. Moreover, the performance of our proposed algorithm is analyzed, including the field size, the time complexity, the encoding complexity at the source node, and the decoding methods. Finally, a random method is introduced for constructing such a family of variable-rate network MDS codes, and a lower bound on the success probability of this random method is given, which shows that this probability will approach to one as the base field size goes to infinity.

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> .

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.

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.

Forecasting Austrian IPOs: An application of linear and neural network error-correction models

In this paper we apply cointegration and Granger-causality analyses to construct linear and neural network error-correction models for an Austrian Initial Public Offerings IndeX (IPOXATX). We use the significant relationship between the IPOXATX and the Austrian Stock Market Index ATX to forecast the IPOXATX. For prediction purposes we apply augmented feedforward neural networks whose architecture is determined by Sequential Network Construction with the Schwartz Information Criterion as an estimator for the prediction risk. Trading based on the forecasts yields results superior to Buy and Hold or Moving Average trading strategies in terms of mean-variance considerations.

Forecasting Austrian IPOs: An application of linear and neural network error‐correction models

In this paper we apply cointegration and Granger-causality analyses to construct linear and neural network error-correction models for an Austrian Initial Public Offerings IndeX (IPOXATX). We use the significant relationship between the IPOXATX and the Austrian Stock Market Index ATX to forecast the IPOXATX. For prediction purposes we apply augmented feedforward neural networks whose architecture is determined by Sequential Network Construction with the Schwartz Information Criterion as an estimator for the prediction risk. Trading based on the forecasts yields results superior to Buy and Hold or Moving Average trading strategies in terms of mean-variance considerations.