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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)
<?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)
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)
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.
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)
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)
We consider the problem of efficient and lossless representation of a multiset of m words drawn with repetition from a set of size 2<sup>n</sup>. One expects that encoding the (unordered) multiset should lead to significant savings in rate as compared to encoding an (ordered) sequence with the same words, since information about the order of words in the… (More)
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)
A probabilistic algorithm is presented for nding a basis of the space of roots of a linearized polynomial L(x) = t X i=0 L i x q i over GF(q n). The complexity of the presented algorithm is O(nt) operations over GF(q n).