27,540 research outputs found
Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM
The use of error-correcting codes for tight control of the peak-to-mean
envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing
(OFDM) transmission is considered in this correspondence. By generalizing a
result by Paterson, it is shown that each q-phase (q is even) sequence of
length 2^m lies in a complementary set of size 2^{k+1}, where k is a
nonnegative integer that can be easily determined from the generalized Boolean
function associated with the sequence. For small k this result provides a
reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new
2^h-ary generalization of the classical Reed-Muller code is then used together
with the result on complementary sets to derive flexible OFDM coding schemes
with low PMEPR. These codes include the codes developed by Davis and Jedwab as
a special case. In certain situations the codes in the present correspondence
are similar to Paterson's code constructions and often outperform them
Design of Geometric Molecular Bonds
An example of a nonspecific molecular bond is the affinity of any positive
charge for any negative charge (like-unlike), or of nonpolar material for
itself when in aqueous solution (like-like). This contrasts specific bonds such
as the affinity of the DNA base A for T, but not for C, G, or another A. Recent
experimental breakthroughs in DNA nanotechnology demonstrate that a particular
nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the
ends of any pair of DNA double-helices) can be used to create specific
"macrobonds" by careful geometric arrangement of many nonspecific blunt ends,
motivating the need for sets of macrobonds that are orthogonal: two macrobonds
not intended to bind should have relatively low binding strength, even when
misaligned.
To address this need, we introduce geometric orthogonal codes that abstractly
model the engineered DNA macrobonds as two-dimensional binary codewords. While
motivated by completely different applications, geometric orthogonal codes
share similar features to the optical orthogonal codes studied by Chung,
Salehi, and Wei. The main technical difference is the importance of 2D geometry
in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and
Multi-Scale Communication
A Systematic Framework for the Construction of Optimal Complete Complementary Codes
The complete complementary code (CCC) is a sequence family with ideal
correlation sums which was proposed by Suehiro and Hatori. Numerous literatures
show its applications to direct-spread code-division multiple access (DS-CDMA)
systems for inter-channel interference (ICI)-free communication with improved
spectral efficiency. In this paper, we propose a systematic framework for the
construction of CCCs based on -shift cross-orthogonal sequence families
(-CO-SFs). We show theoretical bounds on the size of -CO-SFs and CCCs,
and give a set of four algorithms for their generation and extension. The
algorithms are optimal in the sense that the size of resulted sequence families
achieves theoretical bounds and, with the algorithms, we can construct an
optimal CCC consisting of sequences whose lengths are not only almost arbitrary
but even variable between sequence families. We also discuss the family size,
alphabet size, and lengths of constructible CCCs based on the proposed
algorithms
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