Convolutional Codes for Network-Error Correction

Krishnan, Prasad; Rajan, B. Sundar

doi:10.1109/glocom.2009.5425892

Cited by 7 publications

(24 citation statements)

References 21 publications

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“…For a given set of error patterns Φ and for some k < n, a method of constructing rate k/n convolutional codes was given in [7] such that these CNECCs will correct networkerrors which correspond to the patterns in Φ. For a given network with a network code, the definitions for the input and output convolutional code are as follows.…”

Section: B Cneccsmentioning

confidence: 99%

“…It is therefore necessary to study network-error correcting codes which work under small field size conditions. Convolutional network-error correcting codes (CNECCs) were introduced in [7] in the context of coherent network coding for acyclic instantaneous networks. The field size requirement for the CNECCs of [7] is independent of the number of edges in the network and in general much smaller than what is demanded by BNECCs.…”

Section: Introductionmentioning

confidence: 99%

“…Convolutional network-error correcting codes (CNECCs) were introduced in [7] in the context of coherent network coding for acyclic instantaneous networks. The field size requirement for the CNECCs of [7] is independent of the number of edges in the network and in general much smaller than what is demanded by BNECCs. Although the error correcting capability might not be comparable to that offered by BNECCs, the reduction in field size is a considerable advantage in terms of the computation to be performed at each coding node of the network.…”

Section: Introductionmentioning

confidence: 99%

“…The CNECCs of [7] were designed to correct network-errors which correspond to a set Φ of error patterns (subsets of the edge set) once in a certain number of network uses (a network use being the use of the edges of the network to transmit a number of symbols equal to the network code dimension). A similar error model (with Φ being all subsets of the edge set with t edges) was considered in [4]- [6].…”

Section: Introductionmentioning

confidence: 99%

“…However, practical analysis and simulations of BNECCs under a probabilistic error setting is difficult because of the large field size demanded. On the other hand, the CNECCs developed in [7] require small field sizes and thus facilitate analysis. The contributions and organization of this paper are as follows.…”

Section: Introductionmentioning

confidence: 99%

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On network-error correcting convolutional codes under the BSC edge error model

Krishnan

Rajan

2010

2010 IEEE International Symposium on Information Theory

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Abstract-Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error pe(0 ≤ pe < 0.5). We obtain bounds on the performance of such CNECCs based on a modified generating function (the transfer function) of the CNECCs. For a given network, we derive a mathematical condition on how small pe should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low pe and high pe regimes. For the low pe regime, convolutional codes with good distance properties show good performance. For the high pe regime, convolutional codes that have a good slope (the minimum normalized cycle weight) are seen to be good. We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.

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Section: B Cneccsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On network-error correcting convolutional codes under the BSC edge error model

Krishnan

Rajan

2010

2010 IEEE International Symposium on Information Theory

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A Network Delay Factor Model Based on the Hidden Markov Model and Latent Dirichlet Allocation

Yuchi

Yang

et al. 2019

IEEE Access

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Network systems are widely used in today's digital communication systems and applications. Network delay is a very important factor affecting the efficiency and reliability of the system, and researchers often use a model to predict and understand the causes and patterns of delay. For our model, we propose beginning with the Hidden Markov Model (HMM) of the transmission network, which is used to analyze the network's operational situation and to predict the approximate state of the system into the future using the HMM prediction algorithm. Then, employing Latent Dirichlet Allocation (LDA), we put forward the Delay Factor Model (DFM) value for the delay. In the DFM, we need to map the delay's interval to an integer, designated as DII (Delay Interval Integer), and the factors returned define the hidden states of the HMM. From the view of the DFM, DII is generated from a factor and the previous DII randomly. We use the Gibbs Sampling approach to obtain an estimation of the DFM's parameters. By defining the HMM and DFM, we can forecast future delay with high accuracy, and the result can be shown to follow the peaks and troughs of the real operation of the network system's delay patterns.INDEX TERMS Delay factor model, derivation, hidden Markov model, prediction.

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