65,188 research outputs found
Orthogonal Codes for Robust Low-Cost Communication
Orthogonal coding schemes, known to asymptotically achieve the capacity per
unit cost (CPUC) for single-user ergodic memoryless channels with a zero-cost
input symbol, are investigated for single-user compound memoryless channels,
which exhibit uncertainties in their input-output statistical relationships. A
minimax formulation is adopted to attain robustness. First, a class of
achievable rates per unit cost (ARPUC) is derived, and its utility is
demonstrated through several representative case studies. Second, when the
uncertainty set of channel transition statistics satisfies a convexity
property, optimization is performed over the class of ARPUC through utilizing
results of minimax robustness. The resulting CPUC lower bound indicates the
ultimate performance of the orthogonal coding scheme, and coincides with the
CPUC under certain restrictive conditions. Finally, still under the convexity
property, it is shown that the CPUC can generally be achieved, through
utilizing a so-called mixed strategy in which an orthogonal code contains an
appropriate composition of different nonzero-cost input symbols.Comment: 2nd revision, accepted for publicatio
Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding
We determine the optimal rates of universal quantum codes for entanglement
transmission and generation under channel uncertainty. In the simplest scenario
the sender and receiver are provided merely with the information that the
channel they use belongs to a given set of channels, so that they are forced to
use quantum codes that are reliable for the whole set of channels. This is
precisely the quantum analog of the compound channel coding problem. We
determine the entanglement transmission and entanglement-generating capacities
of compound quantum channels and show that they are equal. Moreover, we
investigate two variants of that basic scenario, namely the cases of informed
decoder or informed encoder, and derive corresponding capacity results.Comment: 45 pages, no figures. Section 6.2 rewritten due to an error in
equation (72) of the old version. Added table of contents, added section
'Conclusions and further remarks'. Accepted for publication in
'Communications in Mathematical Physics
Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels
We investigate entanglement transmission over an unknown channel in the
presence of a third party (called the adversary), which is enabled to choose
the channel from a given set of memoryless but non-stationary channels without
informing the legitimate sender and receiver about the particular choice that
he made. This channel model is called arbitrarily varying quantum channel
(AVQC). We derive a quantum version of Ahlswede's dichotomy for classical
arbitrarily varying channels. This includes a regularized formula for the
common randomness-assisted capacity for entanglement transmission of an AVQC.
Quite surprisingly and in contrast to the classical analog of the problem
involving the maximal and average error probability, we find that the capacity
for entanglement transmission of an AVQC always equals its strong subspace
transmission capacity. These results are accompanied by different notions of
symmetrizability (zero-capacity conditions) as well as by conditions for an
AVQC to have a capacity described by a single-letter formula. In he final part
of the paper the capacity of the erasure-AVQC is computed and some light shed
on the connection between AVQCs and zero-error capacities. Additionally, we
show by entirely elementary and operational arguments motivated by the theory
of AVQCs that the quantum, classical, and entanglement-assisted zero-error
capacities of quantum channels are generically zero and are discontinuous at
every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2
and arXiv:1010.0418. Published "Online First" in Communications in
Mathematical Physics, 201
Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation
We determine the secrecy capacities of AVQCs (arbitrarily varying quantum
channels). Both secrecy capacity with average error probability and with
maximal error probability are derived. Both derivations are based on one common
code construction. The code we construct fulfills a stringent secrecy
requirement, which is called the strong code concept. We determine when the
secrecy capacity is a continuous function of the system parameters and
completely characterize its discontinuity points both for average error
criterion and for maximal error criterion. Furthermore, we prove the phenomenon
"super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels
both with zero secrecy capacity, which, if used together, allow secure
transmission with positive capacity. We also discuss the relations between the
entanglement distillation capacity, the entanglement generating capacity, and
the strong subspace transmission capacity for AVQCs.Comment: arXiv admin note: text overlap with arXiv:1702.0348
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