27,951 research outputs found
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
Fault-tolerant gates via homological product codes
A method for the implementation of a universal set of fault-tolerant logical
gates is presented using homological product codes. In particular, it is shown
that one can fault-tolerantly map between different encoded representations of
a given logical state, enabling the application of different classes of
transversal gates belonging to the underlying quantum codes. This allows for
the circumvention of no-go results pertaining to universal sets of transversal
gates and provides a general scheme for fault-tolerant computation while
keeping the stabilizer generators of the code sparse.Comment: 11 pages, 3 figures. v2 (published version): quantumarticle
documentclass, expanded discussion on the conditions for a fault tolerance
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Proofreading tile sets: Error correction for algorithmic self-assembly
For robust molecular implementation of tile-based algorithmic
self-assembly, methods for reducing errors must be developed. Previous
studies suggested that by control of physical conditions, such as
temperature and the concentration of tiles, errors (Īµ) can be reduced
to an arbitrarily low rate - but at the cost of reduced speed (r) for
the self-assembly process. For tile sets directly implementing blocked
cellular automata, it was shown that r ā Ī²Īµ^2 was optimal. Here, we
show that an improved construction, which we refer to as proofreading
tile sets, can in principle exploit the cooperativity of tile assembly reactions
to dramatically improve the scaling behavior to r ā Ī²Īµ and better.
This suggests that existing DNA-based molecular tile approaches may be
improved to produce macroscopic algorithmic crystals with few errors.
Generalizations and limitations of the proofreading tile set construction
are discussed
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