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- Mark F. Flanagan, Vitaly Skachek, Eimear Byrne, Marcus Greferath
- IEEE Transactions on Information Theory
- 2009

A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates LP-based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the ldquomaximum-likelihood (ML) certificaterdquo property. It is also shown that… (More)

- Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
- IEEE Transactions on Information Theory
- 2013

A problem of index coding with side information was first considered by Birk and Kol in 1998. In this study, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied. Error-correcting methods for such a scheme, and their parameters, are investigated. In particular, the following question is discussed: given the… (More)

- Vitaly Skachek
- IEEE Transactions on Information Theory
- 2010

A modification of Ko¿tter-Kschischang codes for random networks is presented (these codes were also studied by Wang in the context of authentication problems). The new codes have higher information rate, while maintaining the same error-correcting capabilities. An efficient error-correcting algorithm is proposed for these codes.

- Farzad Farnoud, Vitaly Skachek, Olgica Milenkovic
- IEEE Transactions on Information Theory
- 2013

<?Pub Dtl?>We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed translocation rank codes account for more general forms of errors that arise in storage… (More)

- Vitaly Skachek, Ron M. Roth
- Des. Codes Cryptography
- 2008

A probabilistic algorithm is presented for finding a basis of the root space of a linearized polynomial

- Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
- IEEE Transactions on Information Theory
- 2012

The min-rank of a digraph was shown to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this paper, the graphs and digraphs of near-extreme min-ranks are studied. Those graphs and digraphs correspond to the ICSI instances having near-extreme transmission… (More)

- Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
- IEEE Transactions on Information Theory
- 2012

Security aspects of the index coding with side information (ICSI) problem are investigated. Building on the results of Bar-Yossef (2006), the properties of linear index codes are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown that the… (More)

- Ron M. Roth, Vitaly Skachek
- IEEE Transactions on Information Theory
- 2006

A construction of expander codes is presented with the following three properties: i) the codes lie close to the Singleton bound, ii) they can be encoded in time complexity that is linear in their code length, and iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace… (More)

- Jens Zumbrägel, Vitaly Skachek, Mark F. Flanagan
- IEEE Transactions on Information Theory
- 2012

For a binary linear code, the pseudocodeword redundancy with respect to the additive white Gaussian noise channel, the binary symmetric channel, or the max-fractional weight is defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of the code. It is shown… (More)

- Faruk Göloglu, Jüri Lember, Ago-Erik Riet, Vitaly Skachek
- 2015 IEEE International Symposium on Information…
- 2015

New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths. Second, several probabilistic lower bounds are developed, which improve on the known lower bounds for large minimum… (More)