Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Tri-State: From Shannon to Galois Fields in Communication Systems

Version 1 : Received: 11 April 2021 / Approved: 12 April 2021 / Online: 12 April 2021 (13:06:38 CEST)

How to cite: Gerck, E. Tri-State: From Shannon to Galois Fields in Communication Systems. Preprints 2021, 2021040306 (doi: 10.20944/preprints202104.0306.v1). Gerck, E. Tri-State: From Shannon to Galois Fields in Communication Systems. Preprints 2021, 2021040306 (doi: 10.20944/preprints202104.0306.v1).

Abstract

Communication, compression of information, transmission of information through noisy channels, interconnecting different information systems, cryptography, gate construction –– these areas all depend on classical information theory. We show that, in classical terms, semantic aspects of communication are not at all irrelevant to the engineering problem, contrary to Shannon, and affect the message intended to be transmitted. This is revisited and captured by an analogy to trust, in that they are essential to the channel (for proper use), but cannot be transferred (under risk of flaws) through that same channel. Information is also described by, at least, a tri-state system — not by binary logic. The trust analogy semantics can be coded as the Curry-Howard relationship, connecting computer code with structural logic, by way of different categories. Two-state and Boolean logic (aka Shannon semantics) was used classically before, with Shannon theory, but without trust analogy semantics – found to be a sine qua non condition. This is now familiar in classical gate construction with physical systems with, e.g., Verilog and SystemVerilog. The applications to computation and quantum theory are further explored. The most fundamental entity in today`s theory of information is proposed to use at least three logical states, not bits, in all applications, including: cyber-physical systems, devices, in computation, and in quantum theory.

Subject Areas

communication; information; tri-state, Galois field; quantum; qubit; qutrit; qudit; trust; interconnect; out-of-band

Comments (1)

Comment 1
Received: 6 May 2021
Commenter: Ed Gerck
The commenter has declared there is no conflict of interests.
Comment: Thanks for feedback. See updated version with title "Tri-state+ Communication Theory"
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