w4kek/WSJT-X
1
0
Fork 0
mirror of https://github.com/saitohirga/WSJT-X.git synced 2024-10-01 01:26:39 -04:00
Code Issues Packages Projects Releases Wiki Activity

A few more minor tweaks to the text.

Browse Source 
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6208 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
This commit is contained in:
Joe Taylor 2015-12-01 14:30:21 +00:00
parent 5c126f0a54
commit 5436682239
1 changed files with 1001 additions and 993 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

36
lib/sfrsd2/sfrsd_paper/sfrsd.lyx
View File

@ -118,7 +118,7 @@ on with a Reed-Solomon code.
, the number of message symbols conveyed by the codeword, and the number , the number of message symbols conveyed by the codeword, and the number
of possible values for each symbol in the codewords. of possible values for each symbol in the codewords.
The codeword length and the number of message symbols are specified using The codeword length and the number of message symbols are specified with
the notation the notation
\begin_inset Formula $(n,k)$ \begin_inset Formula $(n,k)$
\end_inset \end_inset
@ -252,7 +252,11 @@ errors.
\begin_inset Formula $s$ \begin_inset Formula $s$
\end_inset \end_inset
symbols are erased and the remaining (unerased) symbols contain symbols are erased and the remaining
\begin_inset Formula $n-s$
\end_inset
symbols contain
\begin_inset Formula $e$ \begin_inset Formula $e$
\end_inset \end_inset
@ -296,7 +300,7 @@ errors-and-erasures
decoder. decoder.
The possibility of doing errors-and-erasures decoding lies at the heart The possibility of doing errors-and-erasures decoding lies at the heart
of the FT algorithm. of the FT algorithm.
On that foundation we build a capability for using On that foundation we have built a capability for using
\begin_inset Quotes eld \begin_inset Quotes eld
\end_inset \end_inset
@ -304,7 +308,7 @@ soft
\begin_inset Quotes erd \begin_inset Quotes erd
\end_inset \end_inset
information on symbol reliability. information on symbol reliability, thereby producing a soft-decision decoder.
\end_layout \end_layout
\begin_layout Section \begin_layout Section
@ -319,7 +323,7 @@ Do I feel lucky?
\begin_layout Standard \begin_layout Standard
The FT algorithm uses the estimated quality of received symbols to generate The FT algorithm uses the estimated quality of received symbols to generate
lists of symbols considered likely to be in error, thereby enabling reliable lists of symbols considered likely to be in error, thus enabling reliable
decoding of received words with more than 25 errors. decoding of received words with more than 25 errors.
As a specific example, consider a received JT65 word with 23 correct symbols As a specific example, consider a received JT65 word with 23 correct symbols
and 40 errors. and 40 errors.
@ -559,8 +563,8 @@ Examples 1 and 2 show that a random strategy for selecting symbols to erase
incorrect symbols, as before, but suppose we know that 10 symbols are significa incorrect symbols, as before, but suppose we know that 10 symbols are significa
ntly more reliable than the other 53. ntly more reliable than the other 53.
We might therefore protect the 10 most reliable symbols from erasure, and We might therefore protect the 10 most reliable symbols from erasure, selecting
choose erasures from the smaller set of erasures from the smaller set of
\begin_inset Formula $N=53$ \begin_inset Formula $N=53$
\end_inset \end_inset
@ -641,8 +645,8 @@ The FT decoding algorithm
Example 3 shows how reliable information about symbol quality should make Example 3 shows how reliable information about symbol quality should make
it possible to decode received frames having a large number of errors. it possible to decode received frames having a large number of errors.
In practice the number of errors in the received word is unknown, so we In practice the number of errors in the received word is unknown, so we
use a stochastic algorithm to assign a high erasure probability to low-quality use a stochastic algorithm to assign high erasure probability to low-quality
symbols and a relatively low probability to high-quality symbols. symbols and relatively low probability to high-quality symbols.
As illustrated by Example 3, a good choice of these probabilities can increase As illustrated by Example 3, a good choice of these probabilities can increase
the chance of a successful decode by many orders of magnitude. the chance of a successful decode by many orders of magnitude.
\end_layout \end_layout
@ -651,8 +655,7 @@ Example 3 shows how reliable information about symbol quality should make
The FT algorithm uses two quality indices made available by a noncoherent The FT algorithm uses two quality indices made available by a noncoherent
64-FSK demodulator. 64-FSK demodulator.
The demodulator identifies the most likely value for each symbol based The demodulator identifies the most likely value for each symbol based
on which of 64 frequency bins contains the the largest signal-plus-noise on the largest signal-plus-noise power in 64 frequency bins.
power.
The fraction of total power in the two bins containing the largest and The fraction of total power in the two bins containing the largest and
second-largest powers (denoted by second-largest powers (denoted by
\begin_inset Formula $p_{1}$ \begin_inset Formula $p_{1}$
@ -829,7 +832,7 @@ For each received symbol, define the erasure probability as 1.3 times the
a priori a priori
\emph default \emph default
symbol-error probability determined from soft-symbol information symbol-error probability determined from soft-symbol information
\begin_inset Formula $\{p_{1}\textrm{-rank},\, p_{2}/p_{1}\}$ \begin_inset Formula $\{p_{1}\textrm{-rank},\,p_{2}/p_{1}\}$
\end_inset \end_inset
. .
@ -931,6 +934,9 @@ Number of decodes vs.
\begin_layout Itemize \begin_layout Itemize
Probability of successful decode vs. Probability of successful decode vs.
Es/No or S/N in 2500 Hz BW Es/No or S/N in 2500 Hz BW
\end_layout
\begin_layout Standard
\begin_inset Float figure \begin_inset Float figure
wide false wide false
sideways false sideways false
@ -940,6 +946,8 @@ status open
\align center \align center
\begin_inset Graphics \begin_inset Graphics
filename fig_psuccess.pdf filename fig_psuccess.pdf
lyxscale 120
scale 120
\end_inset \end_inset
@ -952,8 +960,8 @@ status open
\begin_layout Plain Layout \begin_layout Plain Layout
Percentage of JT65 messages successfully decoded as a function of SNR in Percentage of JT65 messages successfully decoded as a function of SNR in
2.5 kHz bandwidth. 2.5 kHz bandwidth.
Results are shown for the hard-decision Berlekamp-Massey (BM) and the Franke-Ta Results are shown for the hard-decision Berlekamp-Massey (BM) and the sofft-dec
ylor (FT) decoding algorithms. ision Franke-Taylor (FT) decoding algorithms.
\end_layout \end_layout
\end_inset \end_inset