Negative Beta Encoder
Tohru Kohda, Satoshi Hironaka, and Kazuyuki Aihara

TL;DR
The paper introduces the negative beta-encoder, a novel analog-to-digital converter that leverages a flaky quantiser and Re9nyi map dynamics to achieve exponential accuracy and self-correction, improving quantisation error.
Contribution
It proposes the negative beta-encoder, enhancing the existing beta-encoder with better quantisation error performance and a new theoretical framework based on Re9nyi map dynamics and Markov chains.
Findings
The negative beta-encoder further reduces quantisation error compared to the beta-encoder.
The Re9nyi map analysis explains the self-correction property of the encoder.
A transition matrix with a negative eigenvalue improves quantisation accuracy.
Abstract
A new class of analog-to-digital (A/D) and digital-to-analog (D/A) converters using a flaky quantiser, called the -encoder, has been shown to have exponential bit rate accuracy while possessing a self-correction property for fluctuations of the amplifier factor and the quantiser threshold . The probabilistic behavior of such a flaky quantiser is explained as the deterministic dynamics of the multi-valued R\'enyi map. That is, a sample is always confined to a contracted subinterval while successive approximations of are performed using -expansion even if may vary at each iteration. This viewpoint enables us to get the decoded sample, which is equal to the midpoint of the subinterval, and its associated characteristic equation for recovering which improves the quantisation error by more than when . The invariant…
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Taxonomy
TopicsAnalog and Mixed-Signal Circuit Design · Neural Networks and Applications · Numerical Methods and Algorithms
