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Series in Signal and Information Processing, Vol. 16
edited by Hans-Andrea Loeliger




Matthias Frey
On Analog Decoders and Digitally Corrected Converters.

1. Auflage/1st edition 2006, XVI, 180 Seiten/pages, € 64,00. ISBN 3-86628-074-2

In recent years, the demand for efficient and reliable communication  networks has greatly increased. To satisfy this need, powerful error  correcting codes were introduced. The (iterative) algorithms used for decoding such  modern codes are computationally very demanding and need great computing power to  deliver real-time results. Mobile users, however, demand low-power electronics; the combination of both demands led to an increased interest in analog communication circuits, e.g., in analog decoders for error correcting  codes.

An analog decoder can be understood as a code-representing (factor)  graph mapped on analog silicon, whereas the decoding algorithm (e.g., the  sum-product algorithm) corresponds to the settling behavior of the analog  circuit. The performance gain of analog decoders compared to digital  implementations in terms of speed or power-consumption is believed to be at least a  factor of 100.

The first part of this thesis discusses various implementations of  such analog decoders: Hamming decoders built out of two generations of discrete  softgates, an integrated Hamming decoder and an integrated Reed Muller decoder are presented. An extensive collection of measured error-rate curves of all decoders under various operating conditions prove their full  functionality and demonstrate their behavior under transistor mismatch.

Furthermore, a novel circuit to compute the soft symbols for a PAM or  QAM signal is presented. This simple transistor network blends in nicely  with analog decoders—its outputs are currents proportional to the symbol- likelihoods.

Digital data processing is pervasive, and the need for fast, high resolution and low-power analog-to-digital and digital-to-analog  converters persistent. Highly accurate converters usually require large element to achieve the desired minimal mismatch; large elements however  demand high currents for high speed. This trade-off can be circumvented by using small-sized, yet imprecise, elements and then adding digital post- correction circuitry.

The second part of the thesis is devoted to converters with minimal sized elements. It can be shown, that the effective resolution of a digitally-corrected analog-to-digital converter only weakly depends on the comparator mismatch. This was confirmed by measurements on an integrated flash analog-to-digital converter containing 256 low- precision comparators and achieving an effective resolution of nearly 7 bits. A similar statement holds for current-steering digital-to-analog converters with almost minimal-sized current sources: for a converter containing 12 low-precision current sources and digital post-correction, a effective resolution of more than 10 bits was achieved—virtually  irrespective of the mismatch.

Keywords: Factor graphs, message-passing algorithms, sum-product algorithm, analog non-linear transistor circuits, translinear circuits, soft symbol detection, digital data transmission, analog-to-digital converter, digital-to-analog converter, imprecise elements.

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