
TL;DR
This paper introduces a universal decoding method for noisy codebooks generated by finite-state systems, achieving error performance comparable to optimal ML decoding despite non-uniform codeword distributions.
Contribution
It develops a universal decoding metric based on Lempel-Ziv parsing that works with non-uniform codeword distributions and non-finite-state induced channels.
Findings
Universal decoder matches ML error exponent up to sub-exponential factors.
Decoding metric based on Lempel-Ziv parsing adapts to non-uniform codeword distributions.
Method applicable to biometrical identification systems with noisy codebooks.
Abstract
We consider the topic of universal decoding with a decoder that does not have direct access to the codebook, but only to noisy versions of the various randomly generated codewords, a problem motivated by biometrical identification systems. Both the source that generates the original (clean) codewords, and the channel that corrupts them in generating the noisy codewords, as well as the main channel for communicating the messages, are all modeled by non-unifilar, finite-state systems (hidden Markov models). As in previous works on universal decoding, here too, the average error probability of our proposed universal decoder is shown to be as small as that of the optimal maximum likelihood (ML) decoder, up to a multiplicative factorthat is a sub-exponential function of the block length. It therefore has the same error exponent, whenever the ML decoder has a positive error exponent. The…
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