8,300 research outputs found
Synchronization Strings: Explicit Constructions, Local Decoding, and Applications
This paper gives new results for synchronization strings, a powerful
combinatorial object that allows to efficiently deal with insertions and
deletions in various communication settings:
We give a deterministic, linear time synchronization string
construction, improving over an time randomized construction.
Independently of this work, a deterministic time
construction was just put on arXiv by Cheng, Li, and Wu. We also give a
deterministic linear time construction of an infinite synchronization string,
which was not known to be computable before. Both constructions are highly
explicit, i.e., the symbol can be computed in time.
This paper also introduces a generalized notion we call
long-distance synchronization strings that allow for local and very fast
decoding. In particular, only time and access to logarithmically
many symbols is required to decode any index.
We give several applications for these results:
For any we provide an insdel correcting
code with rate which can correct any fraction
of insdel errors in time. This near linear computational
efficiency is surprising given that we do not even know how to compute the
(edit) distance between the decoding input and output in sub-quadratic time. We
show that such codes can not only efficiently recover from fraction of
insdel errors but, similar to [Schulman, Zuckerman; TransInf'99], also from any
fraction of block transpositions and replications.
We show that highly explicitness and local decoding allow for
infinite channel simulations with exponentially smaller memory and decoding
time requirements. These simulations can be used to give the first near linear
time interactive coding scheme for insdel errors
Importance of Symbol Equity in Coded Modulation for Power Line Communications
The use of multiple frequency shift keying modulation with permutation codes
addresses the problem of permanent narrowband noise disturbance in a power line
communications system. In this paper, we extend this coded modulation scheme
based on permutation codes to general codes and introduce an additional new
parameter that more precisely captures a code's performance against permanent
narrowband noise. As a result, we define a new class of codes, namely,
equitable symbol weight codes, which are optimal with respect to this measure
Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes
We present two methods for the construction of quantum circuits for quantum
error-correcting codes (QECC). The underlying quantum systems are tensor
products of subsystems (qudits) of equal dimension which is a prime power. For
a QECC encoding k qudits into n qudits, the resulting quantum circuit has
O(n(n-k)) gates. The running time of the classical algorithm to compute the
quantum circuit is O(n(n-k)^2).Comment: 18 pages, submitted to special issue of IJFC
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