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S

Series in Signal and Information Processing, Vol. 16
edited by HansAndrea Loeliger
Matthias Frey
On Analog Decoders and Digitally Corrected Converters.
1. Auflage/1^{st} edition 2006, XVI,
180 Seiten/pages, € 64,00. ISBN
3866280742
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 realtime results. Mobile
users, however, demand lowpower 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
coderepresenting (factor) graph mapped on analog silicon, whereas the decoding algorithm (e.g., the
sumproduct 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 powerconsumption 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
errorrate 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 lowpower analogtodigital and digitaltoanalog
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
tradeoff can be circumvented by using smallsized, 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
digitallycorrected analogtodigital converter only
weakly depends on the comparator mismatch. This was confirmed by measurements
on an integrated flash analogtodigital converter
containing 256 low precision comparators and achieving an effective resolution
of nearly 7 bits. A similar statement holds for currentsteering digitaltoanalog converters with almost minimalsized current
sources: for a converter containing 12 lowprecision current sources and
digital postcorrection, a effective resolution of more than 10 bits was
achieved—virtually irrespective of the mismatch.
Keywords: Factor graphs,
messagepassing algorithms, sumproduct algorithm, analog
nonlinear transistor circuits, translinear circuits,
soft symbol detection, digital data transmission, analogtodigital
converter, digitaltoanalog converter, imprecise
elements.
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