Cutoff rate for fixed-composition coding over energy constrained AWGN channels
Author
Oğuz, Nihat Cem
Advisor
Arıkan, Erdal
Date
1990Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
Shannon showed that, under an energy constraint, the ensemble of shell constrained
codes optimizes the cutoff rate for AVVGN channels. Unfortunately, this ensemble is not
very practical since its input alphabet is the entire real line. In this thesis, we consider
the ensemble of fixed-composition codes which satisfy the shell constraint and have a
finite input alphabet.
For a certain four-letter symrnetric input alphabet, the cutoff rates for ensembles of
fixed-composition codes of blocklengths ii]) to 10 are compnti'd for tlie AVVGN channel at
various signal-to-noise ratios. Also an asymptotic analysis of these cutoff rates is carried
out a.s blocklenghth tends to infinity.
These results are compared with the cutoff rates optimized over the independentletters
code ensemble, which is the ensemble ordinarily used in [>ractice. The results of
this comparison show that, for relatively moderate signal-to-noise ratios, it is possible
to achieve cutoff rates within 1-2% of the optimum value by using fixed-composition
codes; whereas, with iudepeiideiit-letters codes, one can get at most within 9-10% of the
optimum value. Thus, fixed-composition codes can provide significant improvements in
cutoff rate in practice, cispiicially for moderate to high signal-to-noise ratios.