155 research outputs found
High-rate self-synchronizing codes
Self-synchronization under the presence of additive noise can be achieved by
allocating a certain number of bits of each codeword as markers for
synchronization. Difference systems of sets are combinatorial designs which
specify the positions of synchronization markers in codewords in such a way
that the resulting error-tolerant self-synchronizing codes may be realized as
cosets of linear codes. Ideally, difference systems of sets should sacrifice as
few bits as possible for a given code length, alphabet size, and
error-tolerance capability. However, it seems difficult to attain optimality
with respect to known bounds when the noise level is relatively low. In fact,
the majority of known optimal difference systems of sets are for exceptionally
noisy channels, requiring a substantial amount of bits for synchronization. To
address this problem, we present constructions for difference systems of sets
that allow for higher information rates while sacrificing optimality to only a
small extent. Our constructions utilize optimal difference systems of sets as
ingredients and, when applied carefully, generate asymptotically optimal ones
with higher information rates. We also give direct constructions for optimal
difference systems of sets with high information rates and error-tolerance that
generate binary and ternary self-synchronizing codes.Comment: 9 pages, no figure, 2 tables. Final accepted version for publication
in the IEEE Transactions on Information Theory. Material presented in part at
the International Symposium on Information Theory and its Applications,
Honolulu, HI USA, October 201
Cyclotomic Constructions of Cyclic Codes with Length Being the Product of Two Primes
Cyclic codes are an interesting type of linear codes and have applications in
communication and storage systems due to their efficient encoding and decoding
algorithms. They have been studied for decades and a lot of progress has been
made. In this paper, three types of generalized cyclotomy of order two and
three classes of cyclic codes of length and dimension
are presented and analysed, where and are two distinct primes.
Bounds on their minimum odd-like weight are also proved. The three
constructions produce the best cyclic codes in certain cases.Comment: 19 page
Parsing a sequence of qubits
We develop a theoretical framework for frame synchronization, also known as
block synchronization, in the quantum domain which makes it possible to attach
classical and quantum metadata to quantum information over a noisy channel even
when the information source and sink are frame-wise asynchronous. This
eliminates the need of frame synchronization at the hardware level and allows
for parsing qubit sequences during quantum information processing. Our
framework exploits binary constant-weight codes that are self-synchronizing.
Possible applications may include asynchronous quantum communication such as a
self-synchronizing quantum network where one can hop into the channel at any
time, catch the next coming quantum information with a label indicating the
sender, and reply by routing her quantum information with control qubits for
quantum switches all without assuming prior frame synchronization between
users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication
in the IEEE Transactions on Information Theor
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