Mathematical Foundations for Information Theory in Diffusion-Based Molecular Communications
نویسندگان
چکیده
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 to 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 sub-class 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 diffusionbased 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 “d̄-continuous”. Other properties of diffusion-based molecular channel such as stationarity or ergodicity are also proven.
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عنوان ژورنال:
- CoRR
دوره abs/1311.4431 شماره
صفحات -
تاریخ انتشار 2013