arXiv subjects

Xuan Guang

Publications and source records attributed to Xuan Guang.

26 records · Page 2Linked to original sources

arXiv2014

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 MDS codes are expected to be used for these different rates. For this purpose, designing a linear network error correction MDS code based on the existing results for each information rate is an efficient solution. In order to solve the problem more efficiently, we present the concept of variable-rate linear network error correction MDS codes, that is, these linear network error correction MDS codes of different rates have the same local encoding kernel at each internal node. Further, we propose an approach to construct such a family of variable-rate network MDS codes and give an algorithm for efficient implementation. This approach saves the storage space for each internal node, and resources and time for the transmission 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 variable-rate network MDS codes and we obtain a lower bound on the success probability of this random method, which shows that this probability will approach to one as the base field size goes to infinity.

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arXiv2014

Distributed Storage Schemes over Unidirectional Ring Networks

In this paper, we study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total original data for each user is proposed, and it is achievable for arbitrary parameters. If a distributed storage scheme can achieve this lower bound with equality for each user, we say it an optimal reconstructing distributed storage scheme (ORDSS). Furthermore, the repair problem for a failed storage node in ORDSSes is under consideration and a tight lower bound on the repair bandwidth for each storage node is obtained. Particularly, we indicate the fact that for any ORDSS, every storage node can be repaired with repair bandwidth achieving the lower bound with equality. In addition, we present an efficient approach to construct ORDSSes for arbitrary parameters by using the concept of Euclidean division. Finally, we take an example to characterize the above approach.

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arXiv2013

Linear Network Error Correction Multicast/Broadcast/Dispersion/Generic Codes

In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding theory, i.e., linear multicast, linear broadcast, linear dispersion, and generic network codes, have been studied extensively. More generally, when channels of communication networks are noisy, information transmission and error correction have to be under consideration simultaneously, and thus these four classes of linear network codes are generalized to linear network error correction (LNEC) coding, and we say them LNEC multicast, broadcast, dispersion, and generic codes, respectively. Furthermore, in order to characterize their efficiency of information transmission and error correction, we propose the (weakly, strongly) extended Singleton bounds for them, and define the corresponding optimal codes, i.e., LNEC multicast/broadcast/dispersion/generic MDS codes, which satisfy the corresponding Singleton bounds with equality. The existences of such MDS codes are discussed in detail by algebraic methods and the constructive algorithms are also proposed.

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arXiv2013

The Failure Probability of Random Linear Network Coding for Networks

In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known. Therefore, random linear network coding has been proposed as an acceptable coding technique for the case that the network topology cannot be utilized completely. Motivated by the fact that different network topological information can be obtained for different practical applications, we study the performance analysis of random linear network coding by analyzing some failure probabilities depending on these different topological information of networks. We obtain some tight or asymptotically tight upper bounds on these failure probabilities and indicate the worst cases for these bounds, i.e., the networks meeting the upper bounds with equality. In addition, if the more topological information of the network is utilized, the better upper bounds are obtained. On the other hand, we also discuss the lower bounds on the failure probabilities.

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arXiv2013

Linear Network Error Correction Multicast/Broadcast/Dispersion Codes

In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to linear network error correction coding, i.e., linear network error correction multicast/broadcast/dispersion codes. We further propose the (weakly, strongly) extended Singleton bounds for these new classes of codes, and define the optimal codes satisfying the corresponding Singleton bounds with equality, which are called multicast/broadcast/dispersion MDS codes respectively. The existence of such codes are proved by an algebraic method and one kind of constructive algorithm is also proposed.

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arXiv2010

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 network error correction coding, especially the Singleton bound. In this paper, following the research line using the extended global encoding kernels proposed in \cite{zhang-correction}, 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 network error correction coding. Motivated partly by the performance analysis of random linear network coding \cite{Ho-etc-random}, we evaluate the different failure probabilities defined in this paper in order to analyze the performance of random linear network error correction coding. 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 \cite{zhang-random}, as well as the upper bound on the field size required for the existence of linear network error correction codes with degradation at most $d$.

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arXiv2010

The Failure Probability at Sink Node of Random Linear Network Coding

In practice, since many communication networks are huge in scale or complicated in structure even dynamic, the predesigned network codes based on the network topology is impossible even if the topological structure is known. Therefore, random linear network coding was proposed as an acceptable coding technique. In this paper, we further study the performance of random linear network coding by analyzing the failure probabilities at sink node for different knowledge of network topology and get some tight and asymptotically tight upper bounds of the failure probabilities. In particular, the worst cases are indicated for these bounds. Furthermore, if the more information about the network topology is utilized, the better upper bounds are obtained. These bounds improve on the known ones. Finally, we also discuss the lower bound of this failure probability and show that it is also asymptotically tight.

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arXiv2010

On Random Linear Network Coding for Butterfly Network

Random linear network coding is a feasible encoding tool for network coding, specially for the non-coherent network, and its performance is important in theory and application. In this letter, we study the performance of random linear network coding for the well-known butterfly network by analyzing the failure probabilities. We determine the failure probabilities of random linear network coding for the well-known butterfly network and the butterfly network with channel failure probability p.

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