The Nonlinear Network Coding and Its Application in Error-Correcting Codes

Zhang, Guangzhi; Cai, Shaobin; Zhang, Dongqiu

doi:10.1007/s11277-017-5109-z

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…However, homomorphic signatures based on cryptographic approaches can correct the propagated error which equals C. However, cryptographic approaches have great complexity, and it is completely impractical in NEC [10]. Although a novel idea using nonlinear network coding seems a promising method to correct more errors, it cannot solve the problem completely just now and this method needs further being studied [11]. Except homomorphic signatures [10], there is no approach that can cope with propagated error which reaches C.…”

Section: The Tough Problem About Error Propagation In Network Codingmentioning

confidence: 99%

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

Zhang

Cai

Zhang

et al. 2018

J Wireless Com Network

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The network coding can spread a single original error over the whole network. The simulation shows that the propagated error mostly all the time pollute just 100% of the received packets at the sink if Hamming distance is adopted. If subspace codes are adopted, usually the propagated error will not pollute 100% of the received packets in the sense of subspace distance. However, it also usually pollutes 90% of received packets which is a high error ratio. Even if the rank code and the subspace code are adopted, these existing schemes based on traditional block codes can correct corrupted errors no more than C/2 because of the limitation of the block coding where C is the max flow min cut. It is an agent to find a dense error correction method in random network coding. List decoding of subspace codes can correct C k -1 errors where k is the size of information. When C k is big, many errors in the sense of subspace distance can be corrected. However, the solution of list decoding is not unique. John Wright proposed a dense error correction technique based on L1 minimization, which can recover nearly 100% of the corrupted observations. In our proposal, the original packets are coded with John Wright's coding matrix, and then, the coded message is coded again with subspace codes. In the sink, the decoding procedures about list decoding of subspace codes and John Wright's scheme are performed. At last, the unique solution is achieved even though there are dense propagated errors in random network coding.

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Section: The Tough Problem About Error Propagation In Network Codingmentioning

confidence: 99%

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

Zhang

Cai

Zhang

et al. 2018

J Wireless Com Network

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“…The poor-quality links in WSN further intensify the crisis of error propagation in network coding. There are fruitful works about network error correction coding for network coding (NEC) [ 6 , 7 , 8 , 9 ]. However, none of the existing works thoroughly solved the error propagation problem in network coding.…”

Section: Introductionmentioning

confidence: 99%

The Application of Social Characteristic and L1 Optimization in the Error Correction for Network Coding in Wireless Sensor Networks

Zhang

Cai

Xiong

2018

Sensors

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One of the remarkable challenges about Wireless Sensor Networks (WSN) is how to transfer the collected data efficiently due to energy limitation of sensor nodes. Network coding will increase network throughput of WSN dramatically due to the broadcast nature of WSN. However, the network coding usually propagates a single original error over the whole network. Due to the special property of error propagation in network coding, most of error correction methods cannot correct more than C/2 corrupted errors where C is the max flow min cut of the network. To maximize the effectiveness of network coding applied in WSN, a new error-correcting mechanism to confront the propagated error is urgently needed. Based on the social network characteristic inherent in WSN and L1 optimization, we propose a novel scheme which successfully corrects more than C/2 corrupted errors. What is more, even if the error occurs on all the links of the network, our scheme also can correct errors successfully. With introducing a secret channel and a specially designed matrix which can trap some errors, we improve John and Yi’s model so that it can correct the propagated errors in network coding which usually pollute exactly 100% of the received messages. Taking advantage of the social characteristic inherent in WSN, we propose a new distributed approach that establishes reputation-based trust among sensor nodes in order to identify the informative upstream sensor nodes. With referred theory of social networks, the informative relay nodes are selected and marked with high trust value. The two methods of L1 optimization and utilizing social characteristic coordinate with each other, and can correct the propagated error whose fraction is even exactly 100% in WSN where network coding is performed. The effectiveness of the error correction scheme is validated through simulation experiments.

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

Zhang,

2024

IEEE Systems Journal

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The Nonlinear Network Coding and Its Application in Error-Correcting Codes

Cited by 4 publications

References 11 publications

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

The combination of sparse learning and list decoding of subspace codes for error correction in random network coding

The Application of Social Characteristic and L1 Optimization in the Error Correction for Network Coding in Wireless Sensor Networks

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

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