134 research outputs found
Entanglement-assisted quantum turbo codes
An unexpected breakdown in the existing theory of quantum serial turbo coding
is that a quantum convolutional encoder cannot simultaneously be recursive and
non-catastrophic. These properties are essential for quantum turbo code
families to have a minimum distance growing with blocklength and for their
iterative decoding algorithm to converge, respectively. Here, we show that the
entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in
the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can
possess both of the aforementioned desirable properties. We give several
examples of EAQ convolutional encoders that are both recursive and
non-catastrophic and detail their relevant parameters. We then modify the
quantum turbo decoding algorithm of Poulin et al., in order to have the
constituent decoders pass along only "extrinsic information" to each other
rather than a posteriori probabilities as in the decoder of Poulin et al., and
this leads to a significant improvement in the performance of unassisted
quantum turbo codes. Other simulation results indicate that
entanglement-assisted turbo codes can operate reliably in a noise regime 4.73
dB beyond that of standard quantum turbo codes, when used on a memoryless
depolarizing channel. Furthermore, several of our quantum turbo codes are
within 1 dB or less of their hashing limits, so that the performance of quantum
turbo codes is now on par with that of classical turbo codes. Finally, we prove
that entanglement is the resource that enables a convolutional encoder to be
both non-catastrophic and recursive because an encoder acting on only
information qubits, classical bits, gauge qubits, and ancilla qubits cannot
simultaneously satisfy them.Comment: 31 pages, software for simulating EA turbo codes is available at
http://code.google.com/p/ea-turbo/ and a presentation is available at
http://markwilde.com/publications/10-10-EA-Turbo.ppt ; v2, revisions based on
feedback from journal; v3, modification of the quantum turbo decoding
algorithm that leads to improved performance over results in v2 and the
results of Poulin et al. in arXiv:0712.288
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
EXIT-chart aided near-capacity quantum turbo code design
High detection complexity is the main impediment in future Gigabit-wireless systems. However, a quantum-based detector is capable of simultaneously detecting hundreds of user signals by virtue of its inherent parallel nature. This in turn requires near-capacity quantum error correction codes for protecting the constituent qubits of the quantum detector against the undesirable environmental decoherence. In this quest, we appropriately adapt the conventional non-binary EXtrinsic Information Transfer (EXIT) charts for quantum turbo codes by exploiting the intrinsic quantum-to-classical isomorphism. The EXIT chart analysis not only allows us to dispense with the time-consuming Monte-Carlo simulations, but also facilitates the design of near-capacity codes without resorting to the analysis of their distance spectra. We have demonstrated that our EXIT chart predictions are in line with the Monte-Carlo simulations results. We have also optimized the entanglement-assisted QTC using EXIT charts, which outperforms the existing distance spectra based QTCs. More explicitly, the performance of our optimized QTC is as close as 0.3 dB to the corresponding hashing bound
EXIT-chart aided code design for symbol-based entanglement-assisted classical communication over quantum channels
Quantum-based transmission is an attractive solution conceived for achieving absolute security. In this quest, we have conceived an EXtrinsic Information Transfer (EXIT) chart aided channel code design for symbol-based entanglement-assisted classical communication over quantum depolarizing channels. Our proposed concatenated code design incorporates a Convolutional Code (CC), a symbol-based Unity Rate Code (URC) and a soft-decision aided 2-qubit Superdense Code (2SD), which is hence referred to as a CC-URC-2SD arrangement. We have optimized our design with the aid of non-binary EXIT charts. Our proposed design operates within 1 dB of the achievable capacity, providing attractive performance gains over its bit-based counterpart. Quantitatively, the bit-based scheme requires 60% more iterations than our symbol-based scheme for the sake of achieving perfect decoding convergence. Furthermore, we demonstrate that the decoding complexity can be reduced by using memory-2 and memory-3 convolutional codes, while still outperforming the bit-based approach<br/
EXIT-chart aided quantum code design improves the normalised throughput of realistic quantum devices
In this contribution, the Hashing bound of Entanglement Assisted Quantum Channels (EAQC) is investigated in the context of quantum devices built from a range of popular materials, such as trapped ion and relying on solid state Nuclear Magnetic Resonance (NMR), which can be modelled as a so-called asymmetric channel. Then, Quantum Error Correction Codes (QECC) are designed based on Extrinsic Information Transfer (EXIT) charts for improving performance when employing these quantum devices. The results are also verified by simulations. Our QECC schemes are capable of operating close to the corresponding Hashing bound
Entanglement-assisted quantum turbo codes
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin , in order to have the constituent decoders pass along only extrinsic information to each other rather than a posteriori probabilities as in the decoder of Poulin , and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them. © 1963-2012 IEEE
A Survey on Quantum Channel Capacities
Quantum information processing exploits the quantum nature of information. It
offers fundamentally new solutions in the field of computer science and extends
the possibilities to a level that cannot be imagined in classical communication
systems. For quantum communication channels, many new capacity definitions were
developed in comparison to classical counterparts. A quantum channel can be
used to realize classical information transmission or to deliver quantum
information, such as quantum entanglement. Here we review the properties of the
quantum communication channel, the various capacity measures and the
fundamental differences between the classical and quantum channels.Comment: 58 pages, Journal-ref: IEEE Communications Surveys and Tutorials
(2018) (updated & improved version of arXiv:1208.1270
- …