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Fix several more typos; round 0.0266 to 0.027.

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git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6218 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
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Joe Taylor 2015-12-02 16:31:52 +00:00
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lib/sfrsd2/sfrsd_paper/sfrsd.lyx
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@ -95,7 +95,8 @@ The JT65 mode has revolutionized amateur-radio weak-signal communication
Since 2004, most JT65 decoders have used the patented Koetter-Vardy (KV)
algebraic soft-decision decoder, licensed to K1JT and implemented in a
closed-source program for use in amateur radio applications.
We describe here a new open-source alternative called the FT algotithm.
We describe here a new open-source alternative called the Franke-Taylor
(FT, or K9AN-K1JT) algorithm.
It is conceptually simple, built around the well-known Berlekamp-Massey
errors-and-erasures algorithm, and performs at least as well as the KV
decoder.
@ -195,7 +196,7 @@ For the JT65 code,
no more than 25 symbol errors.
Any one of several well-known algebraic algorithms, such as the widely
used Berlekamp-Massey (BM) algorithm, can carry out the decoding.
Two steps are ncessarily involved in this process, namely
Two steps are necessarily involved in this process, namely
\end_layout
\begin_layout Enumerate
@ -561,8 +562,8 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase
\begin_inset Formula $X=40$
\end_inset
incorrect symbols, as before, but suppose we know that 10 symbols are significa
ntly more reliable than the other 53.
incorrect symbols, as before, but suppose we know that 10 received symbols
are significantly more reliable than the other 53.
We might therefore protect the 10 most reliable symbols from erasure, selecting
erasures from the smaller set of
\begin_inset Formula $N=53$
@ -573,8 +574,8 @@ ntly more reliable than the other 53.
\begin_inset Formula $s=45$
\end_inset
symbols are chosen randomly in this way, it is still necessary for the
erased symbols to include at least 37 errors, as in Example 2.
symbols are chosen randomly for erasure in this way, it is still necessary
for the erased symbols to include at least 37 errors, as in Example 2.
However, the probabilities are now much more favorable: with
\begin_inset Formula $N=53$
\end_inset
@ -622,7 +623,7 @@ reference "eq:hypergeometric_pdf"
\end_inset
,
\begin_inset Formula $P(x\ge38)=0.0266$
\begin_inset Formula $P(x\ge38)=0.027$
\end_inset
.
@ -638,7 +639,7 @@ name "sec:The-decoding-algorithm"
\end_inset
The FT decoding algorithm
The Franke-Taylor decoding algorithm
\end_layout
\begin_layout Standard
@ -647,8 +648,8 @@ Example 3 shows how reliable information about symbol quality should make
In practice the number of errors in the received word is unknown, so we
use a stochastic algorithm to assign high erasure probability to low-quality
symbols and relatively low probability to high-quality symbols.
As illustrated by Example 3, a good choice of these probabilities can increase
the chance of a successful decode by many orders of magnitude.
As illustrated by Example 3, a good choice of erasure probabilities can
increase the chance of a successful decode by many orders of magnitude.
\end_layout
\begin_layout Standard
@ -656,7 +657,7 @@ The FT algorithm uses two quality indices made available by a noncoherent
64-FSK demodulator.
The demodulator identifies the most likely value for each symbol based
on the largest signal-plus-noise power in 64 frequency bins.
The fraction of total power in the two bins containing the largest and
The fractions of total power in the two bins containing the largest and
second-largest powers (denoted by
\begin_inset Formula $p_{1}$
\end_inset
@ -846,7 +847,7 @@ Make independent stochastic decisions about whether to erase each symbol
\begin_layout Enumerate
Attempt errors-and-erasures decoding by using the BM algorithm and the set
of eraseures determined in step 2.
of erasures determined in step 2.
If the BM decoder is successful go to step 5.
\end_layout