A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum likelihood certificate' property. It is also shown… (More)
—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 systems.… (More)
—The min-rank of a digraph was shown by Bar-Yossef et al. (2006) 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 work, the graphs and digraphs of near-extreme min-ranks are characterized. Those graphs and digraphs correspond to the ICSI instances… (More)
—A modification of Kötter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. 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 area of network… (More)
—A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, 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… (More)
—Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (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… (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)
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).
—We consider the problem of efficient and lossless representation of a multiset of m words drawn with repetition from a set of size 2 n. 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 sequence… (More)
— A construction of graph codes is presented that approaches the Singleton bound as the alphabet size goes to infinity. These codes can be decoded by a combined error-erasure decoder whose time complexity grows linearly with the code length.