361,316 research outputs found
Quantum Channel Capacities Per Unit Cost
Communication over a noisy channel is often conducted in a setting in which
different input symbols to the channel incur a certain cost. For example, for
bosonic quantum channels, the cost associated with an input state is the number
of photons, which is proportional to the energy consumed. In such a setting, it
is often useful to know the maximum amount of information that can be reliably
transmitted per cost incurred. This is known as the capacity per unit cost. In
this paper, we generalize the capacity per unit cost to various communication
tasks involving a quantum channel such as classical communication,
entanglement-assisted classical communication, private communication, and
quantum communication. For each task, we define the corresponding capacity per
unit cost and derive a formula for it analogous to that of the usual capacity.
Furthermore, for the special and natural case in which there is a zero-cost
state, we obtain expressions in terms of an optimized relative entropy
involving the zero-cost state. For each communication task, we construct an
explicit pulse-position-modulation coding scheme that achieves the capacity per
unit cost. Finally, we compute capacities per unit cost for various bosonic
Gaussian channels and introduce the notion of a blocklength constraint as a
proposed solution to the long-standing issue of infinite capacities per unit
cost. This motivates the idea of a blocklength-cost duality, on which we
elaborate in depth.Comment: v3: 18 pages, 2 figure
Capacity per Unit Energy of Fading Channels with a Peak Constraint
A discrete-time single-user scalar channel with temporally correlated
Rayleigh fading is analyzed. There is no side information at the transmitter or
the receiver. A simple expression is given for the capacity per unit energy, in
the presence of a peak constraint. The simple formula of Verdu for capacity per
unit cost is adapted to a channel with memory, and is used in the proof. In
addition to bounding the capacity of a channel with correlated fading, the
result gives some insight into the relationship between the correlation in the
fading process and the channel capacity. The results are extended to a channel
with side information, showing that the capacity per unit energy is one nat per
Joule, independently of the peak power constraint.
A continuous-time version of the model is also considered. The capacity per
unit energy subject to a peak constraint (but no bandwidth constraint) is given
by an expression similar to that for discrete time, and is evaluated for
Gauss-Markov and Clarke fading channels.Comment: Journal version of paper presented in ISIT 2003 - now accepted for
publication in IEEE Transactions on Information Theor
Energy and Sampling Constrained Asynchronous Communication
The minimum energy, and, more generally, the minimum cost, to transmit one
bit of information has been recently derived for bursty communication when
information is available infrequently at random times at the transmitter. This
result assumes that the receiver is always in the listening mode and samples
all channel outputs until it makes a decision. If the receiver is constrained
to sample only a fraction f>0 of the channel outputs, what is the cost penalty
due to sparse output sampling?
Remarkably, there is no penalty: regardless of f>0 the asynchronous capacity
per unit cost is the same as under full sampling, ie, when f=1. There is not
even a penalty in terms of decoding delay---the elapsed time between when
information is available until when it is decoded. This latter result relies on
the possibility to sample adaptively; the next sample can be chosen as a
function of past samples. Under non-adaptive sampling, it is possible to
achieve the full sampling asynchronous capacity per unit cost, but the decoding
delay gets multiplied by 1/f. Therefore adaptive sampling strategies are of
particular interest in the very sparse sampling regime.Comment: Submitted to the IEEE Transactions on Information Theor
Information Rates of ASK-Based Molecular Communication in Fluid Media
This paper studies the capacity of molecular communications in fluid media,
where the information is encoded in the number of transmitted molecules in a
time-slot (amplitude shift keying). The propagation of molecules is governed by
random Brownian motion and the communication is in general subject to
inter-symbol interference (ISI). We first consider the case where ISI is
negligible and analyze the capacity and the capacity per unit cost of the
resulting discrete memoryless molecular channel and the effect of possible
practical constraints, such as limitations on peak and/or average number of
transmitted molecules per transmission. In the case with a constrained peak
molecular emission, we show that as the time-slot duration increases, the input
distribution achieving the capacity per channel use transitions from binary
inputs to a discrete uniform distribution. In this paper, we also analyze the
impact of ISI. Crucially, we account for the correlation that ISI induces
between channel output symbols. We derive an upper bound and two lower bounds
on the capacity in this setting. Using the input distribution obtained by an
extended Blahut-Arimoto algorithm, we maximize the lower bounds. Our results
show that, over a wide range of parameter values, the bounds are close.Comment: 31 pages, 8 figures, Accepted for publication on IEEE Transactions on
Molecular, Biological, and Multi-Scale Communication
Capacity investigation of on-off keying in noncoherent channel settings at low SNR
Onâoff keying (OOK) has repossessed much new research interest to realize green communication for establishing autonomous sensor networks. To realize ultra-low power wireless design, we investigate the minimum energy per bit required for reliable communication of using OOK in a noncoherent channel setting where envelope detection is applied at the receiver. By deïŹning different OOK channels with average transit power constraints, the achievability of the Shannon limit for both cases of using soft and hard decisions at the channel output is evaluated based on the analysis of the capacity per unit-cost at low signal-to-noise ratio. We demonstrate that in phase fading using hard decisions cannot destroy the capacity only if extremely asymmetric OOK inputs are used with a properly chosen threshold. The corresponding pulse-position modulation scheme is explicitly studied and demonstrated to be a Shannon-type solution. Moreover, we also consider a slow Rayleigh fading scenario where the transmitter and receiver have no access to channel realizations.Throughput per unit-cost results are developed to explore the trade-off between power efïŹciency and channel quality for noncoherent OOK using soft and hard decisions
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