10,720 research outputs found
Optimal Feedback Communication via Posterior Matching
In this paper we introduce a fundamental principle for optimal communication
over general memoryless channels in the presence of noiseless feedback, termed
posterior matching. Using this principle, we devise a (simple, sequential)
generic feedback transmission scheme suitable for a large class of memoryless
channels and input distributions, achieving any rate below the corresponding
mutual information. This provides a unified framework for optimal feedback
communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath
scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that
the Horstein scheme indeed attains the BSC capacity, settling a longstanding
conjecture. We further provide closed form expressions for the error
probability of the scheme over a range of rates, and derive the achievable
rates in a mismatch setting where the scheme is designed according to the wrong
channel model. Several illustrative examples of the posterior matching scheme
for specific channels are given, and the corresponding error probability
expressions are evaluated. The proof techniques employed utilize novel
relations between information rates and contraction properties of iterated
function systems.Comment: IEEE Transactions on Information Theor
Information capacity in the weak-signal approximation
We derive an approximate expression for mutual information in a broad class
of discrete-time stationary channels with continuous input, under the
constraint of vanishing input amplitude or power. The approximation describes
the input by its covariance matrix, while the channel properties are described
by the Fisher information matrix. This separation of input and channel
properties allows us to analyze the optimality conditions in a convenient way.
We show that input correlations in memoryless channels do not affect channel
capacity since their effect decreases fast with vanishing input amplitude or
power. On the other hand, for channels with memory, properly matching the input
covariances to the dependence structure of the noise may lead to almost
noiseless information transfer, even for intermediate values of the noise
correlations. Since many model systems described in mathematical neuroscience
and biophysics operate in the high noise regime and weak-signal conditions, we
believe, that the described results are of potential interest also to
researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review
Capacity of Molecular Channels with Imperfect Particle-Intensity Modulation and Detection
This work introduces the particle-intensity channel (PIC) as a model for
molecular communication systems and characterizes the properties of the optimal
input distribution and the capacity limits for this system. In the PIC, the
transmitter encodes information, in symbols of a given duration, based on the
number of particles released, and the receiver detects and decodes the message
based on the number of particles detected during the symbol interval. In this
channel, the transmitter may be unable to control precisely the number of
particles released, and the receiver may not detect all the particles that
arrive. We demonstrate that the optimal input distribution for this channel
always has mass points at zero and the maximum number of particles that can be
released. We then consider diffusive particle transport, derive the capacity
expression when the input distribution is binary, and show conditions under
which the binary input is capacity-achieving. In particular, we demonstrate
that when the transmitter cannot generate particles at a high rate, the optimal
input distribution is binary.Comment: Accepted at IEEE International Symposium on Information Theory (ISIT
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