972 research outputs found
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
Superadditivity of Quantum Channel Coding Rate with Finite Blocklength Joint Measurements
The maximum rate at which classical information can be reliably transmitted
per use of a quantum channel strictly increases in general with , the number
of channel outputs that are detected jointly by the quantum joint-detection
receiver (JDR). This phenomenon is known as superadditivity of the maximum
achievable information rate over a quantum channel. We study this phenomenon
for a pure-state classical-quantum (cq) channel and provide a lower bound on
, the maximum information rate when the JDR is restricted to making
joint measurements over no more than quantum channel outputs, while
allowing arbitrary classical error correction. We also show the appearance of a
superadditivity phenomenon---of mathematical resemblance to the aforesaid
problem---in the channel capacity of a classical discrete memoryless channel
(DMC) when a concatenated coding scheme is employed, and the inner decoder is
forced to make hard decisions on -length inner codewords. Using this
correspondence, we develop a unifying framework for the above two notions of
superadditivity, and show that for our lower bound to to be equal to a
given fraction of the asymptotic capacity of the respective channel,
must be proportional to , where is the respective channel dispersion
quantity.Comment: To appear in IEEE Transactions on Information Theor
Cyclic division algebras: a tool for space-time coding
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank.
Extensive work has been done on Space–Time coding, aiming at
finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to
improve the design of good codes.
The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes
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