68,688 research outputs found
On codes satisfying the double chain condition
AbstractThe double chain condition is described. A number of bounds on the length and weight hierarchy of codes satisfying the double chain condition are given. Constructions of codes satisfying the double chain condition and with trellis complexity 1 or 2 are given
X-code: MDS array codes with optimal encoding
We present a new class of MDS (maximum distance separable) array codes of size nĂn (n a prime number) called X-code. The X-codes are of minimum column distance 3, namely, they can correct either one column error or two column erasures. The key novelty in X-code is that it has a simple geometrical construction which achieves encoding/update optimal complexity, i.e., a change of any single information bit affects exactly two parity bits. The key idea in our constructions is that all parity symbols are placed in rows rather than columns
Universal codes of the natural numbers
A code of the natural numbers is a uniquely-decodable binary code of the
natural numbers with non-decreasing codeword lengths, which satisfies Kraft's
inequality tightly. We define a natural partial order on the set of codes, and
show how to construct effectively a code better than a given sequence of codes,
in a certain precise sense. As an application, we prove that the existence of a
scale of codes (a well-ordered set of codes which contains a code better than
any given code) is independent of ZFC.Comment: 11 page
Strong secrecy on a class of degraded broadcast channels using polar codes
Two polar coding schemes are proposed for the degraded
broadcast channel under different reliability and secrecy
requirements. In these settings, the transmitter wishes to send
multiple messages to a set of legitimate receivers keeping them
masked from a set of eavesdroppers, and individual channels are
assumed to gradually degrade in such a way that each legitimate
receiver has a better channel than any eavesdropper. The layered
decoding structure requires receivers with better channel quality
to reliably decode more messages, while the layered secrecy
structure requires eavesdroppers with worse channel quality to
be kept ignorant of more messages.Postprint (author's final draft
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