3 research outputs found
Mathematical Foundations for Information Theory in Diffusion-Based Molecular Communications
Molecular communication emerges as a promising communication paradigm for
nanotechnology. However, solid mathematical foundations for
information-theoretic analysis of molecular communication have not yet been
built. In particular, no one has ever proven that the channel coding theorem
applies for molecular communication, and no relationship between information
rate capacity (maximum mutual information) and code rate capacity (supremum
achievable code rate) has been established. In this paper, we focus on a major
subclass of molecular communication - the diffusion-based molecular
communication. We provide solid mathematical foundations for information theory
in diffusion-based molecular communication by creating a general
diffusion-based molecular channel model in measure-theoretic form and prove its
channel coding theorems. Various equivalence relationships between statistical
and operational definitions of channel capacity are also established, including
the most classic information rate capacity and code rate capacity. As
byproducts, we have shown that the diffusion-based molecular channel is with
"asymptotically decreasing input memory and anticipation" and "d-continuous".
Other properties of diffusion-based molecular channel such as stationarity or
ergodicity are also proven
ISI-Aware Modeling and Achievable Rate Analysis of the Diffusion Channel
Analyzing the achievable rate of molecular communication via diffusion (MCvD)
inherits intricacies due to its nature: MCvD channel has memory, and the heavy
tail of the signal causes inter symbol interference (ISI). Therefore, using
Shannon's channel capacity formulation for memoryless channel is not
appropriate for the MCvD channel. Instead, a more general achievable rate
formulation and system model must be considered to make this analysis
accurately. In this letter, we propose an effective ISI-aware MCvD modeling
technique in 3-D medium and properly analyze the achievable rate
Capacity of Diffusion based Molecular Communication Networks over LTI-Poisson Channels
In this paper, the capacity of a diffusion based molecular communication
network under the model of a Linear Time Invarient-Poisson (LTI-Poisson)
channel is studied. Introduced in the context of molecular communication, the
LTI-Poisson model is a natural extension of the conventional memoryless Poisson
channel to include memory. Exploiting prior art on linear ISI channels, a
computable finite-letter characterization of the capacity of single-hop
LTI-Poisson networks is provided. Then, the problem of finding more explicit
bounds on the capacity is examined, where lower and upper bounds for the point
to point case are provided. Furthermore, an approach for bounding mutual
information in the low SNR regime using the symmetrized KL divergence is
introduced and its applicability to Poisson channels is shown. To best of our
knowledge, the first non-trivial upper bound on the capacity of Poisson channel
with a maximum transmission constraint in the low SNR regime is found.
Numerical results show that the proposed upper bound is of the same order as
the capacity in the low SNR regime