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Zhen Zhang - One of the best experts on this subject based on the ideXlab platform.

  • linear network Error Correction codes in packet networks
    IEEE Transactions on Information Theory, 2008
    Co-Authors: Zhen Zhang
    Abstract:

    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.

  • Error Correction Capability of random network Error Correction codes
    International Symposium on Information Theory, 2007
    Co-Authors: H. Balli, Xijin Yan, Zhen Zhang
    Abstract:

    In this paper, we study the Error Correction Capability of random linear network Error Correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network Error Correction code and the field size required for the existence of a network Error Correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).

  • ISIT - Error Correction Capability of Random Network Error Correction Codes
    2007 IEEE International Symposium on Information Theory, 2007
    Co-Authors: H. Balli, Xijin Yan, Zhen Zhang
    Abstract:

    In this paper, we study the Error Correction Capability of random linear network Error Correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network Error Correction code and the field size required for the existence of a network Error Correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).

  • Network Error Correction Coding in Packetized Networks
    2006 IEEE Information Theory Workshop - ITW '06 Chengdu, 2006
    Co-Authors: Zhen Zhang
    Abstract:

    This paper, we studies basic properties of network Error Correction codes, their construction, and Correction Capability for various kinds of Errors. Our discussion is confined to the single source multicast case. We define the minimum rank of a network Error Correction code. This plays the same role that minimum distance has played in classical coding theory. We prove the existence of codes that can correct Errors up to the full Error Correction Capability in singleton bound. Even when the rank of the Error is higher than the Error Correction Capability, we show that the Error can be corrected with very high probability under reasonable assumptions

Michael W Marcellin - One of the best experts on this subject based on the ideXlab platform.

  • Error Correction Capability of column weight three ldpc codes under the gallager a algorithm part ii
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

  • On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the guaranteed Error Correction Capability of ? -left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3 ?/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed Error Correction Capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed Error Correction Capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case Errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.

  • Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

  • Guaranteed Error Correction Capability of codes on graphs
    2009 Information Theory and Applications Workshop, 2009
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Michael W Marcellin
    Abstract:

    The guaranteed Error Correction Capability of left regular LDPC codes under different hard decision decision algorithms is investigated. A summary of recent results relating the column weight and girth of the Tanner graph to the guaranteed Error Correction Capability is provided. The intuition behind expander based arguments and their potential to derive new results for column-weight-three codes is provided.

  • Error Correction Capability of Column-Weight-Three LDPC Codes: Part II
    IEEE Transactions on Information Theory, 2009
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error cor- rection Capability of column-weight-three LDPC codes is inves- tigated. Specifically, it is shown that the Gallager A algorithm can correct g/2 1 Errors in g/2 iterations on a Tanner graph of girth g � 10. Iterative message passing algorithms for decoding low- density parity-check (LDPC) codes (?) operate by passing messages along the edges of a graphical representation of the code known as the Tanner graph (?). These algorithms are optimal when the underlying graph is a tree (see (?),(?) for general theory of LDPC codes), but in the presence of cycles, the decoding becomes sub-optimal and there exist low-weight patterns known as near codewords (?) or trapping sets (?) uncorrectable by the decoder. It is now well established that the trapping sets lead to Error floor in the high signal-to-no ise (SNR) region (see (?) for a list of references). While it is generally known that high girth codes have better performance in the Error floor region, the exact relation between the girt h and the slope of the frame Error rate (FER) curve in the Error floor region is unknown. In this paper, we consider the Error Correction Capability of column-weight-three LDPC codes under the Gallager A decoding algorithm as a function of the girth of the underlying Tanner graph of the code. We also show how the results can be extended to the parallel bit flipping algorithm (?), (?), a low-complexity iterative algorithm which does not belong to the class of message passing algorithms. Gallager showed that the minimum distance of ensembles of (dv, dc)-regular LDPC codes with dc > dv ≥ 3, grows linearly with the code length. While this implies that there exist codes in these ensembles capable of correcting a linear number of Errors in the code length under maximum-likelihood (ML) decoding, it does not necessarily imply the same for sub-optimal decoding algorithms. Zyablov and Pinsker (?) initialed the study of guaranteed Error Correction capabil ity of LDPC codes. They showed that almost all the codes in the regular code ensembles with dv ≥ 5 are capable of correcting a linear number of Errors in the code length under

Bane Vasic - One of the best experts on this subject based on the ideXlab platform.

  • Check-hybrid GLDPC codes: Systematic elimination of trapping sets and guaranteed Error Correction Capability
    Transactions on Emerging Telecommunications Technologies, 2016
    Co-Authors: Vida Ravanmehr, Mehrdad Khatami, David Declercq, Bane Vasic
    Abstract:

    In this paper, we propose a new approach to construct a class of check-hybrid generalized low-density parity-check CH-GLDPC codes, which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2-Error-correcting component code. Specifically, we follow 2 main purposes to construct the check-hybrid codes; first, on the basis of the knowledge of trapping sets of an LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping decoder corrects the Errors on a trapping set. The second purpose is to minimize the rate loss through finding the minimum number of such critical checks. We also present an algorithm to find critical checks in a trapping set of a column-weight 3 LDPC code of girth 8 and then provide upper bounds on the minimum number of such critical checks such that the decoder corrects all Error patterns on elementary trapping sets. Guaranteed Error Correction Capability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC code in which each variable node is connected to 2 super checks corresponding to a 2-Error-correcting component code corrects up to 5 Errors. The results are also extended to column-weight 4 LDPC codes of girth 6. Finally, we investigate eliminating of trapping sets of a column-weight 3 LDPC code of girth 8 using the Gallager B decoding algorithm.

  • Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and Guaranteed Error Correction Capability
    arXiv: Information Theory, 2016
    Co-Authors: Vida Ravanmehr, Mehrdad Khatami, David Declercq, Bane Vasic
    Abstract:

    In this paper, we propose a new approach to construct a class of check-hybrid generalized low-density parity-check (CH-GLDPC) codes which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2-Error correcting component code. Specifically, we follow two main purposes to construct the check-hybrid codes; first, based on the knowledge of the trapping sets of the global LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping (PBF) decoder corrects the Errors on a trapping set and hence eliminates the trapping set. The second purpose is to minimize the rate loss caused by replacing the super checks through finding the minimum number of such critical checks. We also present an algorithm to find critical checks in a trapping set of column-weight 3 LDPC code and then provide upper bounds on the minimum number of such critical checks such that the decoder corrects all Error patterns on elementary trapping sets. Moreover, we provide a fixed set for a class of constructed check-hybrid codes. The guaranteed Error Correction Capability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC code in which each variable node is connected to 2 super checks corresponding to a 2-Error correcting component code corrects up to 5 Errors. The results are also extended to column-weight 4 LDPC codes. Finally, we investigate the eliminating of trapping sets of a column-weight 3 LDPC code using the Gallager B decoding algorithm and generalize the results obtained for the PBF for the Gallager B decoding algorithm.

  • Barcodes for DNA sequencing with guaranteed Error Correction Capability
    Electronics Letters, 2011
    Co-Authors: Anantha Raman Krishnan, Megan Sweeney, J Vasic, David W. Galbraith, Bane Vasic
    Abstract:

    Advances in DNA sequencing have resulted in instruments of remarkable performance, including extraordinary base read rates, and enormous sequencing depths. Sample throughput, nevertheless, remains slow, a situation that could be alleviated through sample multiplexing, with the incorporation of DNA barcodes serving to identify the different samples. Given the existence of finite sequencing Error rates, reported is the design from BCH codes of DNA barcodes that provide guaranteed Correction of Errors within these barcodes.

  • Error Correction Capability of column weight three ldpc codes under the gallager a algorithm part ii
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

  • Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

Shashi Kiran Chilappagari - One of the best experts on this subject based on the ideXlab platform.

  • Error Correction Capability of column weight three ldpc codes under the gallager a algorithm part ii
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

  • Error Correction Capability of Column-Weight-Three LDPC Codes Under the Gallager A Algorithm—Part II
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error Correction Capability of column-weight-three LDPC codes under the Gallager A algorithm is investigated. It is shown that a column-weight-three LDPC code with Tanner graph of girth g ? 10 can correct all Error patterns with up to (g/2-1) Errors in at most g/2 iterations of the Gallager A algorithm. For codes with Tanner graphs of girth g ? 8, it is shown that girth alone cannot guarantee Correction of all Error patterns with up to (g/2-1) Errors under the Gallager A algorithm. Sufficient conditions to correct (g/2-1) Errors are then established by studying trapping sets.

  • On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes
    IEEE Transactions on Information Theory, 2010
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the guaranteed Error Correction Capability of ? -left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3 ?/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed Error Correction Capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed Error Correction Capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case Errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.

  • Guaranteed Error Correction Capability of codes on graphs
    2009 Information Theory and Applications Workshop, 2009
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Michael W Marcellin
    Abstract:

    The guaranteed Error Correction Capability of left regular LDPC codes under different hard decision decision algorithms is investigated. A summary of recent results relating the column weight and girth of the Tanner graph to the guaranteed Error Correction Capability is provided. The intuition behind expander based arguments and their potential to derive new results for column-weight-three codes is provided.

  • Error Correction Capability of Column-Weight-Three LDPC Codes: Part II
    IEEE Transactions on Information Theory, 2009
    Co-Authors: Shashi Kiran Chilappagari, Bane Vasic, Dung Viet Nguyen, Michael W Marcellin
    Abstract:

    The relation between the girth and the Error cor- rection Capability of column-weight-three LDPC codes is inves- tigated. Specifically, it is shown that the Gallager A algorithm can correct g/2 1 Errors in g/2 iterations on a Tanner graph of girth g � 10. Iterative message passing algorithms for decoding low- density parity-check (LDPC) codes (?) operate by passing messages along the edges of a graphical representation of the code known as the Tanner graph (?). These algorithms are optimal when the underlying graph is a tree (see (?),(?) for general theory of LDPC codes), but in the presence of cycles, the decoding becomes sub-optimal and there exist low-weight patterns known as near codewords (?) or trapping sets (?) uncorrectable by the decoder. It is now well established that the trapping sets lead to Error floor in the high signal-to-no ise (SNR) region (see (?) for a list of references). While it is generally known that high girth codes have better performance in the Error floor region, the exact relation between the girt h and the slope of the frame Error rate (FER) curve in the Error floor region is unknown. In this paper, we consider the Error Correction Capability of column-weight-three LDPC codes under the Gallager A decoding algorithm as a function of the girth of the underlying Tanner graph of the code. We also show how the results can be extended to the parallel bit flipping algorithm (?), (?), a low-complexity iterative algorithm which does not belong to the class of message passing algorithms. Gallager showed that the minimum distance of ensembles of (dv, dc)-regular LDPC codes with dc > dv ≥ 3, grows linearly with the code length. While this implies that there exist codes in these ensembles capable of correcting a linear number of Errors in the code length under maximum-likelihood (ML) decoding, it does not necessarily imply the same for sub-optimal decoding algorithms. Zyablov and Pinsker (?) initialed the study of guaranteed Error Correction capabil ity of LDPC codes. They showed that almost all the codes in the regular code ensembles with dv ≥ 5 are capable of correcting a linear number of Errors in the code length under

H. Balli - One of the best experts on this subject based on the ideXlab platform.

  • Error Correction Capability of random network Error Correction codes
    International Symposium on Information Theory, 2007
    Co-Authors: H. Balli, Xijin Yan, Zhen Zhang
    Abstract:

    In this paper, we study the Error Correction Capability of random linear network Error Correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network Error Correction code and the field size required for the existence of a network Error Correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).

  • ISIT - Error Correction Capability of Random Network Error Correction Codes
    2007 IEEE International Symposium on Information Theory, 2007
    Co-Authors: H. Balli, Xijin Yan, Zhen Zhang
    Abstract:

    In this paper, we study the Error Correction Capability of random linear network Error Correction codes (Z. Zhang, 2006). We derive bounds on the probability mass function of the minimum distance of a random network Error Correction code and the field size required for the existence of a network Error Correction code with a given degradation, which is the difference between the highest possible minimum distance in the Singleton bound and the minimum distance of the code. The main tool that we use to study these problems is an improved bound on the failure probability of random linear network codes that at one or more sinks, the source messages are not decodable. This problem was originally studied in T. Ho et al. (2006).