18,745 research outputs found
Entanglement-assisted capacity of constrained quantum channel
In this paper we fill the gap in previous works by proving the formula for
entanglement-assisted capacity of quantum channel with additive constraint
(such as bosonic Gaussian channel). The main tools are the coding theorem for
classical-quantum constrained channels and a finite dimensional approximation
of the input density operators for entanglement-assisted capacity. The new
version contains improved formulation of sufficient conditions under which
suprema in the capacity formulas are attained.Comment: Extended version of paper presented at Quantum Informatics Symposium,
Zvenigorod, 1-4.10.200
The price of certainty: "waterslide curves" and the gap to capacity
The classical problem of reliable point-to-point digital communication is to
achieve a low probability of error while keeping the rate high and the total
power consumption small. Traditional information-theoretic analysis uses
`waterfall' curves to convey the revolutionary idea that unboundedly low
probabilities of bit-error are attainable using only finite transmit power.
However, practitioners have long observed that the decoder complexity, and
hence the total power consumption, goes up when attempting to use sophisticated
codes that operate close to the waterfall curve.
This paper gives an explicit model for power consumption at an idealized
decoder that allows for extreme parallelism in implementation. The decoder
architecture is in the spirit of message passing and iterative decoding for
sparse-graph codes. Generalized sphere-packing arguments are used to derive
lower bounds on the decoding power needed for any possible code given only the
gap from the Shannon limit and the desired probability of error. As the gap
goes to zero, the energy per bit spent in decoding is shown to go to infinity.
This suggests that to optimize total power, the transmitter should operate at a
power that is strictly above the minimum demanded by the Shannon capacity.
The lower bound is plotted to show an unavoidable tradeoff between the
average bit-error probability and the total power used in transmission and
decoding. In the spirit of conventional waterfall curves, we call these
`waterslide' curves.Comment: 37 pages, 13 figures. Submitted to IEEE Transactions on Information
Theory. This version corrects a subtle bug in the proofs of the original
submission and improves the bounds significantl
Capacity Analysis for Continuous Alphabet Channels with Side Information, Part I: A General Framework
Capacity analysis for channels with side information at the receiver has been
an active area of interest. This problem is well investigated for the case of
finite alphabet channels. However, the results are not easily generalizable to
the case of continuous alphabet channels due to analytic difficulties inherent
with continuous alphabets. In the first part of this two-part paper, we address
an analytical framework for capacity analysis of continuous alphabet channels
with side information at the receiver. For this purpose, we establish novel
necessary and sufficient conditions for weak* continuity and strict concavity
of the mutual information. These conditions are used in investigating the
existence and uniqueness of the capacity-achieving measures. Furthermore, we
derive necessary and sufficient conditions that characterize the capacity value
and the capacity-achieving measure for continuous alphabet channels with side
information at the receiver.Comment: Submitted to IEEE Trans. Inform. Theor
Resolvability on Continuous Alphabets
We characterize the resolvability region for a large class of point-to-point
channels with continuous alphabets. In our direct result, we prove not only the
existence of good resolvability codebooks, but adapt an approach based on the
Chernoff-Hoeffding bound to the continuous case showing that the probability of
drawing an unsuitable codebook is doubly exponentially small. For the converse
part, we show that our previous elementary result carries over to the
continuous case easily under some mild continuity assumption.Comment: v2: Corrected inaccuracies in proof of direct part. Statement of
Theorem 3 slightly adapted; other results unchanged v3: Extended version of
camera ready version submitted to ISIT 201
Joint Source-Channel Coding over a Fading Multiple Access Channel with Partial Channel State Information
In this paper we address the problem of transmission of correlated sources
over a fast fading multiple access channel (MAC) with partial channel state
information available at both the encoders and the decoder. We provide
sufficient conditions for transmission with given distortions. Next these
conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal
power allocation strategy and compare the strategy with various levels of
channel state information.
Keywords: Fading MAC, Power allocation, Partial channel state information,
Correlated sources.Comment: 7 Pages, 3 figures. To Appear in IEEE GLOBECOM, 200
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