22,331 research outputs found
Optimization of Information Rate Upper and Lower Bounds for Channels with Memory
We consider the problem of minimizing upper bounds and maximizing lower
bounds on information rates of stationary and ergodic discrete-time channels
with memory. The channels we consider can have a finite number of states, such
as partial response channels, or they can have an infinite state-space, such as
time-varying fading channels. We optimize recently-proposed information rate
bounds for such channels, which make use of auxiliary finite-state machine
channels (FSMCs). Our main contribution in this paper is to provide iterative
expectation-maximization (EM) type algorithms to optimize the parameters of the
auxiliary FSMC to tighten these bounds. We provide an explicit, iterative
algorithm that improves the upper bound at each iteration. We also provide an
effective method for iteratively optimizing the lower bound. To demonstrate the
effectiveness of our algorithms, we provide several examples of partial
response and fading channels, where the proposed optimization techniques
significantly tighten the initial upper and lower bounds. Finally, we compare
our results with an improved variation of the \emph{simplex} local optimization
algorithm, called \emph{Soblex}. This comparison shows that our proposed
algorithms are superior to the Soblex method, both in terms of robustness in
finding the tightest bounds and in computational efficiency. Interestingly,
from a channel coding/decoding perspective, optimizing the lower bound is
related to increasing the achievable mismatched information rate, i.e., the
information rate of a communication system where the decoder at the receiver is
matched to the auxiliary channel, and not to the original channel.Comment: Submitted to IEEE Transactions on Information Theory, November 24,
200
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
On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions
In this paper, the capacity of the additive white Gaussian noise (AWGN)
channel, affected by time-varying Wiener phase noise is investigated. Tight
upper and lower bounds on the capacity of this channel are developed. The upper
bound is obtained by using the duality approach, and considering a specific
distribution over the output of the channel. In order to lower-bound the
capacity, first a family of capacity-achieving input distributions is found by
solving a functional optimization of the channel mutual information. Then,
lower bounds on the capacity are obtained by drawing samples from the proposed
distributions through Monte-Carlo simulations. The proposed capacity-achieving
input distributions are circularly symmetric, non-Gaussian, and the input
amplitudes are correlated over time. The evaluated capacity bounds are tight
for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be
used to quantify the capacity. Specifically, the bounds follow the well-known
AWGN capacity curve at low SNR, while at high SNR, they coincide with the
high-SNR capacity result available in the literature for the phase-noise
channel.Comment: IEEE Transactions on Communications, 201
Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction
In fiber-optic communications, evaluation of mutual information (MI) is still
an open issue due to the unavailability of an exact and mathematically
tractable channel model. Traditionally, lower bounds on MI are computed by
approximating the (original) channel with an auxiliary forward channel. In this
paper, lower bounds are computed using an auxiliary backward channel, which has
not been previously considered in the context of fiber-optic communications.
Distributions obtained through two variations of the stochastic digital
backpropagation (SDBP) algorithm are used as auxiliary backward channels and
these bounds are compared with bounds obtained through the conventional digital
backpropagation (DBP). Through simulations, higher information rates were
achieved with SDBP, {which can be explained by the ability of SDBP to account
for nonlinear signal--noise interactionsComment: 8 pages, 5 figures, accepted for publication in Journal of Lightwave
Technolog
Upper Bounds on the Capacities of Noncontrollable Finite-State Channels with/without Feedback
Noncontrollable finite-state channels (FSCs) are FSCs in which the channel
inputs have no influence on the channel states, i.e., the channel states evolve
freely. Since single-letter formulae for the channel capacities are rarely
available for general noncontrollable FSCs, computable bounds are usually
utilized to numerically bound the capacities. In this paper, we take the
delayed channel state as part of the channel input and then define the {\em
directed information rate} from the new channel input (including the source and
the delayed channel state) sequence to the channel output sequence. With this
technique, we derive a series of upper bounds on the capacities of
noncontrollable FSCs with/without feedback. These upper bounds can be achieved
by conditional Markov sources and computed by solving an average reward per
stage stochastic control problem (ARSCP) with a compact state space and a
compact action space. By showing that the ARSCP has a uniformly continuous
reward function, we transform the original ARSCP into a finite-state and
finite-action ARSCP that can be solved by a value iteration method. Under a
mild assumption, the value iteration algorithm is convergent and delivers a
near-optimal stationary policy and a numerical upper bound.Comment: 15 pages, Two columns, 6 figures; appears in IEEE Transaction on
Information Theor
Information transmission over an amplitude damping channel with an arbitrary degree of memory
We study the performance of a partially correlated amplitude damping channel
acting on two qubits. We derive lower bounds for the single-shot classical
capacity by studying two kinds of quantum ensembles, one which allows to
maximize the Holevo quantity for the memoryless channel and the other allowing
the same task but for the full-memory channel. In these two cases, we also show
the amount of entanglement which is involved in achieving the maximum of the
Holevo quantity. For the single-shot quantum capacity we discuss both a lower
and an upper bound, achieving a good estimate for high values of the channel
transmissivity. We finally compute the entanglement-assisted classical channel
capacity.Comment: 17 pages, 7 figure
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