From ff54b5d59525f748616388e95236a8e7c9b92656 Mon Sep 17 00:00:00 2001
From: Joe Taylor <k1jt@arrl.org>
Date: Fri, 8 Jan 2016 20:27:21 +0000
Subject: [PATCH] Fix the FT algorithm description.  Add hinted algorithm, and
 a few edits. Still needed: Updated Figure 4, and text for Section 7.

git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/wsjtx@6363 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
---
 lib/ftrsd/ftrsd_paper/ftrsd.lyx | 187 ++++++++++++++++++++++++--------
 1 file changed, 140 insertions(+), 47 deletions(-)

diff --git a/lib/ftrsd/ftrsd_paper/ftrsd.lyx b/lib/ftrsd/ftrsd_paper/ftrsd.lyx
index b11d44e1f..4defeeec5 100644
--- a/lib/ftrsd/ftrsd_paper/ftrsd.lyx
+++ b/lib/ftrsd/ftrsd_paper/ftrsd.lyx
@@ -91,7 +91,7 @@ name "sec:Introduction-and-Motivation"
 
 \end_inset
 
-Introduction and Motivation
+Background and Motivation
 \end_layout
 
 \begin_layout Standard
@@ -139,14 +139,15 @@ WSJT-X
 \emph default
 , widely used for amateur weak-signal communication with JT65 and other
  specialized digital modes.
- The program is freely available 
+ The program is freely available and licensed under the GNU General Public
+ License 
 \begin_inset CommandInset citation
 LatexCommand cite
 key "wsjt"
 
 \end_inset
 
- and licensed under the GNU General Public License.
+.
 \end_layout
 
 \begin_layout Standard
@@ -991,7 +992,11 @@ Here the
 \end_inset
 
 's are the symbol values for the candidate codeword being tested.
- The correct JT65 codeword produces a value for 
+ 
+\end_layout
+
+\begin_layout Standard
+The correct JT65 codeword produces a value for 
 \begin_inset Formula $u$
 \end_inset
 
@@ -1051,16 +1056,12 @@ where
 
 \end_inset
 
-
-\end_layout
-
-\begin_layout Standard
 In contrast, the expected value and standard deviation of the 
 \begin_inset Formula $u$
 \end_inset
 
--metric for a randomly selected incorrect codeword (selected from a population
- of all 
+-metric for an incorrect codeword (randomly selected from a population of
+ all 
 \begin_inset Quotes eld
 \end_inset
 
@@ -1099,6 +1100,10 @@ i.e.
 
 \end_inset
 
+
+\end_layout
+
+\begin_layout Standard
 If 
 \begin_inset Formula $u$
 \end_inset
@@ -1138,11 +1143,12 @@ If
 \end_layout
 
 \begin_layout Standard
-If no tested codeword is correct or the signal-to-noise ratio 
+If the signal-to-noise ratio 
 \begin_inset Formula $y$
 \end_inset
 
- is too small for decoding to be possible, the ratio 
+ is too small for decoding to be possible, or for some other reason the
+ correct codeword is never presented as a candidate, the ratio 
 \begin_inset Formula $r=u_{2}/u_{1}$
 \end_inset
 
@@ -1308,23 +1314,31 @@ If
 \end_inset
 
  by setting 
-\begin_inset Formula $u_{2}=u_{1}$
+\begin_inset Formula $u_{2}=u_{1}.$
 \end_inset
 
- and then set 
-\begin_inset Formula $u_{1}=u$
+ Then set 
+\begin_inset Formula $u_{1}=u,$
 \end_inset
 
-.
+ 
+\begin_inset Formula $d_{1}=d_{s},$
+\end_inset
+
+ and 
+\begin_inset Formula $X_{1}=X.$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Enumerate
 If 
-\begin_inset Formula $X<X_{0}$
+\begin_inset Formula $X_{1}<X_{0}$
 \end_inset
 
  and 
-\begin_inset Formula $d_{s}<d_{0}$
+\begin_inset Formula $d_{s}<D_{0}$
 \end_inset
 
 , go to step 11.
@@ -1345,11 +1359,11 @@ If the number of trials is less than the timeout limit
 
 \begin_layout Enumerate
 If 
-\begin_inset Formula $d_{s}<d_{1}$
+\begin_inset Formula $d_{1}<D_{1}$
 \end_inset
 
  and 
-\begin_inset Formula $r<r_{1},$
+\begin_inset Formula $r=u2/u1<r_{1},$
 \end_inset
 
  go to step 11.
@@ -1447,18 +1461,18 @@ The FT algorithm is completely general: with equal sensitivity it recovers
 much
 \emph default
  smaller list of messages (say, a few thousand messages or less) that we
- can guess might be among the most likely ones to be received.
+ might suppose would be among the most likely ones to be received.
  One such situation exists when making short ham-radio contacts that exchange
  minimal information including callsigns, signal reports, perhaps Maidenhead
  locators, and acknowledgments.
  On the EME path or a VHF or UHF band with limited geographical coverage,
- the most likely received messages often originate from callsigns that have
+ the most common received messages often originate from callsigns that have
  been decoded before.
  Saving a list of previously decoded callsigns and associated locators makes
  it easy to generate lists of hypothetical messages and their corresponding
  codewords at very little computational expense.
- The resulting candidate codewords can be tested in the same way as those
- generated by the probabilistic method described in Section 
+ The resulting candidate codewords can be tested in almost the same way
+ as those generated by the probabilistic method described in Section 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "sec:The-decoding-algorithm"
@@ -1492,45 +1506,124 @@ deep search
 For hinted decoding we again invoke a ratio threshold test, but in this
  case we use it to answer a more limited question.
  Over the full list of messages considered likely, we want to know whether
- 
-\begin_inset Formula $r=u_{2}/u_{1}$
-\end_inset
-
-, the ratio of second-largest to largest
-\begin_inset Formula $u$
-\end_inset
-
--metric, is small enough for us to be confident the codeword associated
- with 
+ a suitable metric can distinguish with confidence between the one correct
+ codeword and all others in the generated list.
+ We again find that the most effective metric involves a comparison of 
 \begin_inset Formula $u_{1}$
 \end_inset
 
- is the one that was transmitted.
- Once again we will set an empirical limit, say 
-\begin_inset Formula $r_{2},$
+ and 
+\begin_inset Formula $u_{2},$
 \end_inset
 
- that is small enough to establish adequate confidence, while still ensuring
- that false decodes are rare.
+ the largest and second-largest values of total signal-plus-noise power
+ among all the tested codewords.
+ Once again the criterion for comparison is chosen empirically to maximize
+ the number of correct decodes while ensuring that false decodes are rare.
  Because tested candidate codewords are drawn from a list typically no longer
  than a few thousand, rather than 
 \begin_inset Formula $2^{72},$
 \end_inset
 
- 
-\begin_inset Formula $r_{2}$
-\end_inset
-
- can be a more relaxed limit than that used in the FT algorithm.
- For the limited subset of messages suggested by operator experience to
- be likely, hinted decodes can be obtained at lower signal levels than required
- for the full universe of 
+ the limit can can be more relaxed than that used in the FT algorithm.
+ THus, for the limited subset of messages suggested by operator experience
+ to be likely, hinted decodes can be obtained at lower signal levels than
+ required for the full universe of 
 \begin_inset Formula $2^{72}$
 \end_inset
 
  possible messages.
 \end_layout
 
+\begin_layout Standard
+\begin_inset Float algorithm
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Pseudo-code for hinted decoding
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+Generate a list of 
+\begin_inset Formula $L$
+\end_inset
+
+ codewords considered likely to be received.
+ Set a pointer to the start of this list.
+\end_layout
+
+\begin_layout Enumerate
+Fetch the next candidate codeword and calculate its metric 
+\begin_inset Formula $u.$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+If 
+\begin_inset Formula $u$
+\end_inset
+
+ is the largest found so far, presevre any previous value of 
+\begin_inset Formula $u_{1}$
+\end_inset
+
+ by setting 
+\begin_inset Formula $u_{2}=u_{1},$
+\end_inset
+
+ then set 
+\begin_inset Formula $u_{1}=u.$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Enumerate
+If the number of tested codewords is less than 
+\begin_inset Formula $L,$
+\end_inset
+
+ go to step 2.
+\end_layout
+
+\begin_layout Enumerate
+If 
+\begin_inset Formula $r=u2/u1<r_{2},$
+\end_inset
+
+ go to step 7.
+\end_layout
+
+\begin_layout Enumerate
+Otherwise, declare hinted-decoding failure and exit.
+\end_layout
+
+\begin_layout Enumerate
+An acceptable hinted decode has been found.
+ Declare a successful result and return this codeword.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 \begin_inset CommandInset label
 LatexCommand label