Merged master 8748
This commit is contained in:
Jordan Sherer
@@ -1,50 +0,0 @@
|
||||
// Status=review
|
||||
.Main Window:
|
||||
- Select *FT8* on the *Mode* menu.
|
||||
- Set Tx and Rx frequencies to 1200 Hz.
|
||||
- Double-click on *Erase* to clear both text windows.
|
||||
|
||||
.Wide Graph Settings:
|
||||
|
||||
- *Bins/Pixel* = 4, *Start* = 200 Hz, *N Avg* = 2
|
||||
- Adjust the width of the Wide Graph window so that the upper
|
||||
frequency limit is approximately 2600 Hz.
|
||||
|
||||
.Open a Wave File:
|
||||
|
||||
- Select *File | Open* and navigate to
|
||||
+...\save\samples\FT8\170709_135615.wav+. The waterfall and decoded
|
||||
text window should look something like the following screen shots:
|
||||
|
||||
[[X15]]
|
||||
image::170709_135615.wav.png[align="left",alt="Wide Graph Decode 170709_135615"]
|
||||
|
||||
image::ft8_decodes.png[align="left"]
|
||||
|
||||
- Click with the mouse anywhere on the waterfall display. The green Rx
|
||||
frequency marker will jump to your selected frequency, and the Rx
|
||||
frequency control on the main window will be updated accordingly.
|
||||
|
||||
- Do the same thing with the Shift key held down. Now the red Tx
|
||||
frequency marker and its associated control on the main window will
|
||||
follow your frequency selections.
|
||||
|
||||
- Do the same thing with the Ctrl key held down. Now the both colored
|
||||
markers and both spinner controls will follow your selections.
|
||||
|
||||
- Double-clicking at any frequency on the waterfall does all the
|
||||
things just described and also invokes the decoder in a small range
|
||||
around that frequency.
|
||||
|
||||
- Now double-click on any of the the lines of decoded text in the main
|
||||
window. Unless you have *My Call* set to K1JT or KY7M on the
|
||||
*Settings -> General* tab, all three lines will show the same
|
||||
behavior, setting both RxFreq and TxFreq to the frequency of the
|
||||
selected message. However, if MyCall is set to K1JT then clicking on
|
||||
a message directed to K1JT will move only the Rx frequency setting.
|
||||
This behavior is desirable so that you will not inadvertently change
|
||||
your Tx frequency to that of a tail-ender who called you somewhere
|
||||
else in the FT8 subband.
|
||||
|
||||
IMPORTANT: When finished with this Tutorial, don't forget to re-enter
|
||||
your own callsign as *My Call* on the *Settings | General* tab.
|
||||
@@ -1,371 +0,0 @@
|
||||
<HTML><HEAD>
|
||||
|
||||
<TITLE> Creating a Parity Check Matrix </TITLE>
|
||||
|
||||
</HEAD><BODY>
|
||||
|
||||
|
||||
<H1> Creating a Parity Check Matrix </H1>
|
||||
|
||||
<P>This software deals only with linear block codes for binary (ie,
|
||||
modulo-2, GF(2)) vectors. The set of valid codewords for a linear
|
||||
code can be specified by giving a <I>parity check matrix</I>,
|
||||
<B>H</B>, with <I>M</I> rows and <I>N</I> columns. The valid
|
||||
codewords are the vectors, <B>x</B>, of length <I>N</I>, for which
|
||||
<B>Hx</B>=<B>0</B>, where all arithmetic is done modulo-2. Each row
|
||||
of <B>H</B> represents a parity check on a subset of the bits in
|
||||
<B>x</B>; all these parity checks must be satisfied for <B>x</B> to be
|
||||
a codeword. Note that the parity check matrix for a given code (ie,
|
||||
for a given set of valid codewords) is not unique, even after
|
||||
eliminating rows of <B>H</B> that are redundant because they are
|
||||
linear combinations of other rows.
|
||||
|
||||
<P>This software stores parity check matrices in files in a sparse
|
||||
format. These parity-check files are <I>not</I> human-readable
|
||||
(except by using the <A HREF="#print-pchk"><TT>print-pchk</TT></A>
|
||||
program). However, they <I>are</I> readable on a machine with a
|
||||
different architecture than they were written on.
|
||||
|
||||
<P>Some LDPC software by David MacKay and others uses the
|
||||
<A HREF="http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html">alist
|
||||
format</A> for parity check matrices. Two programs for converting
|
||||
between this format and the format for sparse parity check matrices
|
||||
used by this software are provided.
|
||||
|
||||
|
||||
<A NAME="ldpc"><H2>Methods for constructing LDPC codes</H2></A>
|
||||
|
||||
<P>This software is primarily intended for experimentation with Low
|
||||
Density Parity Check (LDPC) codes. These codes can be constructed by
|
||||
various methods, which generally involve some random selection of
|
||||
where to put 1s in a parity check matrix. Any such method for
|
||||
constructing LDPC codes will have the property that it produces parity
|
||||
check matrices in which the number of 1s in a column is approximately
|
||||
the same (perhaps on average) for any size parity check matrix. For a
|
||||
given code rate, these matrices therefore become increasingly sparse
|
||||
as the length of a codeword, and hence the number of parity checks,
|
||||
increases.
|
||||
|
||||
<P>Many methods for constructing LDPC matrices are described in the
|
||||
<A HREF="refs.html">references</A>. Two simple methods are currently
|
||||
implemented by this software, both of which operate according to the
|
||||
following scheme:
|
||||
<OL>
|
||||
<LI> Create a preliminary parity check matrix by one of the methods.
|
||||
<LI> Add 1s to the parity check matrix in order to avoid rows that have no
|
||||
1s in them, and hence are redundant, or which have only one 1 in them,
|
||||
in which case the corresponding codeword bits will always be zero.
|
||||
The places within such a row to add these 1s are selected randomly.
|
||||
<LI> If the preliminary parity check matrix constructed in step (1) had
|
||||
an even number of 1s in each column, add further 1s to avoid the problem
|
||||
that this will cause the rows to add to zero, and hence at least
|
||||
one check will be redundant. Up to two 1s are added (since it is also
|
||||
undesirable for the sum of the rows to have only one 1 in it), at
|
||||
positions selected randomly from the entire matrix. However, the
|
||||
number of 1s to add in this step is reduced by the number already added
|
||||
in step (2). (Note that although redundant checks are not disastrous,
|
||||
they are better avoided; see the discussion of <A HREF="dep-H.html">linear
|
||||
dependence in parity check matrices</A>.)
|
||||
<LI> If requested, try to eliminate
|
||||
situations where a pair of columns both have 1s in a particular pair of
|
||||
rows, which correspond to cycles of length four in the factor graph of
|
||||
the parity check matrix. When such a situation is detected, one of the
|
||||
1s involved is moved randomly within its column. This continues until
|
||||
no such situations remain, or until 10 passes over all columns have
|
||||
failed to eliminate all such situations.
|
||||
</OL>
|
||||
|
||||
<P>The <I>evencol</I> method is the simplest way of performing step
|
||||
(1) of the above procedure. For each column of the parity check
|
||||
matrix, independently, it places a specified number of 1s in positions
|
||||
selected uniformly at random, with the only constraint being that
|
||||
these 1s be in distinct rows. Note that despite the name, the columns
|
||||
do not have to have the same number of 1s - a distribution over
|
||||
several values for the number of 1s in a column can be specified
|
||||
instead. Such codes with different-weight columns are sometimes
|
||||
better than codes in which every column has the same weight.
|
||||
|
||||
<P>The <I>evenboth</I> method also puts a specified number of 1s in
|
||||
each column, but it tries as well to keep the numbers of 1s in the
|
||||
rows approximately the same. Initially, it creates indicators for all
|
||||
the 1s that will be required, and assigns these 1s to rows as evenly
|
||||
as it can, favouring earlier rows if an exactly even split is not
|
||||
possible. It then assigns 1s to successive columns by selecting
|
||||
randomly, without replacement, from this initial supply of 1s, subject
|
||||
only to the constraint that the 1s assigned to a column must be in
|
||||
distinct rows. If at some point it is impossible to put the required
|
||||
number of 1s in a column by picking from the 1s remaining, a 1 is set
|
||||
in that column without reference to other columns, creating a possible
|
||||
unevenness.
|
||||
|
||||
<P>Note that regardless of how evenly 1s are distributed in the
|
||||
preliminary parity check matrix created in step (1), steps (2) and (3)
|
||||
can make the numbers of 1s in the both rows and columns be uneven, and
|
||||
step (4), if done, can make the numbers of 1s in rows be uneven.
|
||||
|
||||
|
||||
<P><A NAME="make-pchk"><HR><B>make-pchk</B>: Make a parity check
|
||||
matrix by explicit specification.
|
||||
|
||||
<BLOCKQUOTE><PRE>
|
||||
make-pchk <I>pchk-file n-checks n-bits row</I>:<I>col ...</I>
|
||||
</PRE></BLOCKQUOTE>
|
||||
|
||||
<P>Creates a file named <TT><I>pchk-file</I></TT> in
|
||||
which it stores a parity check matrix with <TT><I>n-checks</I></TT>
|
||||
rows and <TT><I>n-bits</I></TT> columns. This parity check matrix
|
||||
consists of all 0s except for 1s at the <I>row</I>:<I>col</I>
|
||||
positions listed. Rows and columns are numbered starting at zero.
|
||||
This program is intended primarily for testing and demonstration
|
||||
purposes.
|
||||
|
||||
<P><B>Example:</B> The well-known Hamming code with codewords of
|
||||
length <I>N</I>=7 and with <I>M</I>=3 parity checks can be can be
|
||||
created as follows:
|
||||
<UL><PRE>
|
||||
<LI>make-pchk ham7.pchk 3 7 0:0 0:3 0:4 0:5 1:1 1:3 1:4 1:6 2:2 2:4 2:5 2:6
|
||||
</PRE></UL>
|
||||
|
||||
|
||||
<P><A NAME="alist-to-pchk"><HR><B>alist-to-pchk</B>: Convert a parity
|
||||
check matrix from alist format to the sparse matrix format used by
|
||||
this software.
|
||||
|
||||
<BLOCKQUOTE><PRE>
|
||||
alist-to-pchk [ -t ] <I>alist-file pchk-file</I>
|
||||
</PRE></BLOCKQUOTE>
|
||||
|
||||
<P>Converts a parity check matrix in
|
||||
<A HREF="http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html">alist
|
||||
format</A> stored in the file named <TT><I>alist-file</I></TT> to
|
||||
the sparse matrix format used by this software, storing it in the
|
||||
file named <TT><I>pchk-file</I></TT>.
|
||||
|
||||
<P>If the <B>-t</B> option is given, the transpose of the parity check
|
||||
matrix in <TT><I>alist-file</I></TT> is stored in the
|
||||
<TT><I>pchk-file</I></TT>.
|
||||
|
||||
<P>Any zeros indexes in the alist file are ignored, so that alist files
|
||||
with zero padding (as required in the specification) are accepted,
|
||||
but files without this zero padding are also accepted. Newlines
|
||||
are ignored by <TT>alist-to-pchk</TT>, so no error is reported if
|
||||
the set of indexes in a row or column description are not those
|
||||
on a single line.
|
||||
|
||||
|
||||
<P><A NAME="pchk-to-alist"><HR><B>pchk-to-alist</B>: Convert a parity
|
||||
check matrix to alist format.
|
||||
|
||||
<BLOCKQUOTE><PRE>
|
||||
pchk-to-alist [ -t ] [ -z ] <I>pchk-file alist-file</I>
|
||||
</PRE></BLOCKQUOTE>
|
||||
|
||||
<P>Converts a parity check matrix stored in the sparse matrix format
|
||||
used by this software, in the file named <TT><I>pchk-file</I></TT>, to
|
||||
the <A
|
||||
HREF="http://www.inference.phy.cam.ac.uk/mackay/codes/alist.html">alist
|
||||
format</A>, storing it in the file named <TT><I>alist-file</I></TT>.
|
||||
|
||||
<P>If the <B>-t</B> option is given, the transpose of the parity check
|
||||
matrix is converted to alist format.
|
||||
|
||||
<P>If the number of 1s is not
|
||||
the same for each row or each column, the alist format specification
|
||||
says that the list of indexes of 1s for each row or column should
|
||||
be padded with zeros to the maximum number of indexes. By default,
|
||||
<TT>pchk-to-alist</TT> does this, but output of these 0s can be
|
||||
suppressed by specifying the <B>-z</B> option. (The <TT>alist-to-pchk</TT>
|
||||
program will accept alist files produced with or without the <B>-z</B>
|
||||
option.)
|
||||
|
||||
|
||||
<P><A NAME="print-pchk"><HR><B>print-pchk</B>: Print a parity check matrix.
|
||||
|
||||
<BLOCKQUOTE><PRE>
|
||||
print-pchk [ -d ] [ -t ] <I>pchk-file</I>
|
||||
</PRE></BLOCKQUOTE>
|
||||
|
||||
<P>Prints a human-readable representation of the parity check matrix stored
|
||||
in <TT><I>pchk-file</I></TT>.
|
||||
The <B>-d</B> option causes the matrix to be printed in a dense
|
||||
format, even though parity check matrices are always stored in the
|
||||
file in a sparse format. If the <B>-t</B> option is present, what is
|
||||
printed is the transpose of the parity check matrix.
|
||||
|
||||
<P>The sparse display format consists of one line for every row of the
|
||||
matrix, consisting of the row number, a colon, and the column numbers
|
||||
at which 1s are located (possibly none). Row and columns numbers
|
||||
start at zero. No attempt is made to wrap long lines.
|
||||
|
||||
<P>The dense display is the obvious array of 0s and 1s. Long lines
|
||||
are not wrapped.
|
||||
|
||||
<P><B>Example</B>: The parity check matrix for the Hamming code created
|
||||
by the example for <A HREF="#make-pchk"><TT>make-pchk</TT></A> would print
|
||||
as follows:
|
||||
<UL><PRE>
|
||||
<LI>print-pchk ham7.pchk
|
||||
|
||||
Parity check matrix in ham7.pchk (sparse format):
|
||||
|
||||
0: 0 3 4 5
|
||||
1: 1 3 4 6
|
||||
2: 2 4 5 6
|
||||
|
||||
<LI>print-pchk -d ham7.pchk
|
||||
|
||||
Parity check matrix in ham7.pchk (dense format):
|
||||
|
||||
1 0 0 1 1 1 0
|
||||
0 1 0 1 1 0 1
|
||||
0 0 1 0 1 1 1
|
||||
</PRE></UL>
|
||||
|
||||
|
||||
<P><A NAME="make-ldpc"><HR><B>make-ldpc</B>: Make a low density parity
|
||||
check matrix, by random generation.
|
||||
|
||||
<BLOCKQUOTE><PRE>
|
||||
make-ldpc <I>pchk-file n-checks n-bits seed method</I>
|
||||
</PRE>
|
||||
<BLOCKQUOTE>
|
||||
where <TT><I>method</I></TT> is one of the following:
|
||||
<BLOCKQUOTE><PRE>
|
||||
evencol <I>checks-per-col</I> [ no4cycle ]
|
||||
|
||||
evencol <I>checks-distribution</I> [ no4cycle ]
|
||||
|
||||
evenboth <I>checks-per-col</I> [ no4cycle ]
|
||||
|
||||
evenboth <I>checks-distribution</I> [ no4cycle ]
|
||||
</PRE></BLOCKQUOTE>
|
||||
</BLOCKQUOTE>
|
||||
</BLOCKQUOTE>
|
||||
|
||||
<P>Creates a Low Density Parity Check matrix with
|
||||
<TT><I>n-checks</I></TT> rows and <TT><I>n-bits</I></TT> columns. The
|
||||
parity check matrix will be generated pseudo-randomly by the indicated
|
||||
method, using a pseudo-random number stream determined by <TT><I>seed</I></TT>.
|
||||
The actual random number seed used is 10 times <TT><I>seed</I></TT> plus 1,
|
||||
so as to avoid using the same stream as any of the other programs.
|
||||
|
||||
<P>Two methods are currently available for creating the LDPC matrix,
|
||||
specified by <TT>evencol</TT> or <TT>evenboth</TT>. Both methods
|
||||
produce a matrix in which the number of 1s in each column is
|
||||
approximately <TT><I>checks-per-col</I></TT>, or varies from column
|
||||
to column according the the <TT><I>checks-distribution</I></TT>.
|
||||
The <TT>evenboth</TT> method also tries to make the number of checks per row be
|
||||
approximately uniform; if this is not achieved, a message saying that
|
||||
how many bits were placed unevenly is displayed on standard error.
|
||||
|
||||
<P>For both methods, the <TT>no4cycle</TT> option will cause cycles of
|
||||
length four in the factor graph representation of the code to be
|
||||
eliminated (if possible). A message is displayed on standard error if
|
||||
this is not achieved.
|
||||
|
||||
<P>A <TT><I>checks-distribution</I></TT> has the form
|
||||
<BLOCKQUOTE><PRE>
|
||||
<I>prop</I>x<I>count</I>/<I>prop</I>x<I>count</I>/...
|
||||
</PRE></BLOCKQUOTE>
|
||||
Here, <TT><I>prop</I></TT> is a proportion of columns that have the
|
||||
associated <TT><I>count</I></TT>. The proportions need not sum to one,
|
||||
since they will be automatically normalized. For example, <TT>0.3x4/0.2x5</TT>
|
||||
specifies that 60% of the columns will contain four 1s and 40% will
|
||||
contain five 1s.
|
||||
|
||||
<P>See the <A HREF="#ldpc">discussion above</A> for more details
|
||||
on how these methods construct LDPC matrices.
|
||||
|
||||
<P><B>Example 1:</B> The <TT>make-ldpc</TT> command below creates
|
||||
a 20 by 40 low density parity check matrix with three 1s per
|
||||
column and six 1s per row, using random seed 1. The matrix
|
||||
is then printed in sparse format
|
||||
using <A HREF="#print-pchk">print-pchk</A>.
|
||||
<UL><PRE>
|
||||
<LI>make-ldpc ldpc.pchk 20 40 1 evenboth 3
|
||||
<LI>print-pchk ldpc.pchk
|
||||
|
||||
Parity check matrix in ldpc.pchk (sparse format):
|
||||
|
||||
0: 10 14 18 27 38 39
|
||||
1: 2 3 5 11 27 30
|
||||
2: 15 19 20 21 24 26
|
||||
3: 2 4 25 28 32 38
|
||||
4: 7 9 12 22 33 34
|
||||
5: 5 6 21 22 26 32
|
||||
6: 1 4 13 24 25 28
|
||||
7: 1 14 28 29 30 36
|
||||
8: 11 13 22 23 32 37
|
||||
9: 6 8 13 20 31 33
|
||||
10: 0 3 24 29 31 38
|
||||
11: 7 12 15 16 17 23
|
||||
12: 3 16 29 34 35 39
|
||||
13: 0 8 10 18 36 37
|
||||
14: 6 11 18 20 35 39
|
||||
15: 0 7 14 16 25 37
|
||||
16: 2 4 9 19 30 31
|
||||
17: 5 9 10 17 19 23
|
||||
18: 8 15 17 21 26 27
|
||||
19: 1 12 33 34 35 36
|
||||
</PRE></UL>
|
||||
|
||||
<P><B>Example 2:</B> The two <TT>make-ldpc</TT> commands
|
||||
below both create a 20 by 40 low density parity check matrix with 30%
|
||||
of columns with two 1s, 60% of columns with three 1s, and 10% of
|
||||
columns with seven 1s. The transpose of the parity check matrix
|
||||
is then printed in sparse format.
|
||||
<UL><PRE>
|
||||
<LI>make-ldpc ldpc.pchk 20 40 1 evenboth 0.3x2/0.6x3/0.1x7
|
||||
<LI>make-ldpc ldpc.pchk 20 40 1 evenboth 3x2/6x3/1x7
|
||||
<LI>print-pchk -t ldpc.pchk
|
||||
|
||||
Transpose of parity check matrix in ldpc.pchk (sparse format):
|
||||
|
||||
0: 13 16
|
||||
1: 9 18
|
||||
2: 1 10
|
||||
3: 3 15
|
||||
4: 4 14
|
||||
5: 14 17
|
||||
6: 4 5
|
||||
7: 1 8
|
||||
8: 0 4
|
||||
9: 9 14
|
||||
10: 5 8
|
||||
11: 6 16
|
||||
12: 2 12 19
|
||||
13: 3 17 18
|
||||
14: 2 16 17
|
||||
15: 2 11 18
|
||||
16: 12 13 19
|
||||
17: 7 13 18
|
||||
18: 2 5 11
|
||||
19: 10 12 14
|
||||
20: 1 8 16
|
||||
21: 10 18 19
|
||||
22: 3 6 17
|
||||
23: 7 11 12
|
||||
24: 1 2 19
|
||||
25: 0 6 7
|
||||
26: 5 8 15
|
||||
27: 1 4 7
|
||||
28: 6 13 19
|
||||
29: 3 4 11
|
||||
30: 3 8 17
|
||||
31: 4 5 9
|
||||
32: 0 10 15
|
||||
33: 7 11 13
|
||||
34: 8 12 19
|
||||
35: 0 2 10
|
||||
36: 0 5 9 11 15 17 18
|
||||
37: 0 1 2 6 7 14 16
|
||||
38: 0 1 3 9 12 13 15
|
||||
39: 3 6 9 10 14 15 16
|
||||
</PRE></UL>
|
||||
|
||||
<HR>
|
||||
|
||||
<A HREF="index.html">Back to index for LDPC software</A>
|
||||
|
||||
</BODY></HTML>
|
||||
|
||||
@@ -1,30 +0,0 @@
|
||||
<table cellpadding=5>
|
||||
<tr>
|
||||
<th align="right">Click on</th>
|
||||
<th align="left">Action</th>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">Waterfall:</td>
|
||||
<td><b>Click</b> to set the Rx frequency.<br/>
|
||||
<b>Shift-click</b> to set Tx frequency.<br/>
|
||||
<b>Ctrl-click</b> to set Rx and Tx frequencies.<br/>
|
||||
<b>Double-click</b> to decode at resulting Rx frequency.<br/>
|
||||
If <b>Lock Tx=Rx</b> is checked all actions set Tx/Rx.
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">Decoded text:</td>
|
||||
<td><b>Double-click</b> to copy second callsign to Dx Call,<br/>
|
||||
locator to Dx Grid; change Rx and Tx frequencies to<br/>
|
||||
decoded signal's frequency; generate standard messages.<br/>
|
||||
If first callsign is your own, Tx frequency is not<br/>
|
||||
changed unless Ctrl is held down when double-clicking.
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right">Erase button:</td>
|
||||
<td><b>Click</b> to erase QSO window.<br/>
|
||||
<b>Double-click</b> to erase QSO and Band Activity windows.
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
Reference in New Issue
Block a user