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SymbolIntersecting Codes
Roth, Ron M.; Seroussi, Gadiel
HPL2004117
Keyword(s): errorcorrecting codes; broadcast channels; codes over rings; ReedSolomon codes; subfield subcodes; Kronecker sum of matrices
Abstract: Please note: This abstract contains mathematical formula which cannot be represented here. We consider codes consisting of arrays over an alphabet F, in which certain intersecting subsets of n x m coordinates are required to form codewords of length n in prescribed codes over the alphabet F^{m}. Two specific cases are studied. In the first case, referred to as a singlyintersecting coding scheme, the user data is mapped into n x (2m1) arrays over an alphabet F, such that the n x m subarray that consists of the left (respectively, right) m columns forms a codeword of a prescribed code of length n over F^{m}; in particular, the center column is shared by the left and right subarrays. Bounds are obtained on the achievable redundancy region of singlyintersecting coding schemes, and constructions are presented which approachand sometimes meet these bounds. It is shown that singlyintersecting coding schemes can be applied in a certain model of broadcast channels to guarantee reliable communication. The second setting, referred to as a fullyintersecting coding scheme, maps the user data into n x m x m threedimensional arrays in which parallel n x m subarrays are all codewords of the same prescribed code over F^{m}. Bounds and constructions are presented for these codes, with the analysis based on representing the n x m x m arrays as vectors over certain algebras on m x m matrices.
35 Pages
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