A.A. Kreshchuk
Simple Asymptotic Bounds on Statistical Decoder Error
Rate
Statistical
decoders are one of the most robust decoders for positional modulations like
FSK and PPM. As we show in this work they are applicable to any (unknown) channels
that have non-zero distance between received signals. This makes it possible to
use statistical decoders in NOMA random access communication systems with bad
Channel State Information. In this work we consider the problem of data
transmission over unknown memoryless channels. To the
author's knowledge this problem was not studied in literature till now. We
propose repetition Kautz-Singleton codes and
statistical decoders as a solution to this problem. To estimate the performance
of the proposed solution we propose a lower and an upper asymptotic bounds on
error rate for statistical decoder. These bounds are evaluated for Kolmogorov-Smirnov goodness-of-fit criteria and compared to
a computer simulation. The lower bound seems to be close to the simulation
result. The upper bound is not that close to the simulation result but it still
holds. To the author's knowledge this is the first technique to derive bounds
on error rate for any distance-based statistical decoder. These bounds for the Kolmogorov-Smirnov goodness-of-fit criterion also show that
the error rate should be inversely proportional to the square root of code
distance. Other goodness-of-fit criteria might yield asymptotically better
results.
KEYWORDS: coded FSK, goodness-of-fit criterion, unknown
channel, Kautz-Singleton code