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Date: Sun, 4 Jan 2015 14:22:09 -0500
Message-ID: <CAMFjj714F0oUBvY9gPseH_5ha=Jev_c_nDgfMMh2aFKCFawFdQ@mail.gmail.com>
From: Warren Ziegler <wd2xgj@gmail.com>
To: rsgb_lf_group <rsgb_lf_group@blacksheep.org>
Subject: Re: VLF: Transatlantic messages at 8822Hz
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Paul, Dex, Markus,

     First congratulations Dex and Paul !

Second, it has been many years since my graduate work in mathematics at
Courant, and then it was oriented toward PDE's, fluid mechanics, complex
variable, and mathematical methods.
What is the best text for getting up to speed on convolutional coding and
Viterbi decoding?

73 & tnx Warren


On Sun, Jan 4, 2015 at 10:11 AM, Markus Vester <markusvester@aol.com> wrote:

>  Big congratulations again to Paul and Dex!
>
> What Paul described in unpretentious and matter-of-fact words should
> really be regarded as a major achievement. It has been a well-deserved
> fruit of several months of effort, and there were a number of difficulties
> to be overcome. As I was lucky to be included in the preceding email
> exchange, I had the chance to witness milestones and setbacks during the
> process.
>
> Most members of the LF group will appreciate the challenges to Dex on the
> sub-9kHz transmit side, dealing with large coils and high voltage,
> realizing accurate GPS-derived frequencies and sub-second bit timing, and
> last not least being able to leave the signal on air reliably for many
> hours.
>
> The information processing side handled solely by Paul surely presented an
> even higher hurdle: In the first place, he searched and found a small
> handful of "good" FEC codes. The search involved extensive simulations on
> powerful multicore computers hired from the Amazon cloud. Then the soft
> Viterby decoding of a potential receive signal is also computer intensive,
> especially for longer messages. There need to be numerous trials while
> optimising reference phase evolution, bit timing, and antenna weights.
>
> Perhaps the most challenging part was guessing appropriate parameters
> before a transmission, ie. how many characters should be sent in which
> amount of time. Although some experience had been gained from carrier
> measurements during previous nights, ionospheric and atmospheric variations
> make it hard to predict SNR accurately enough if you want to exploit the
> channel capacity to the last couple of dBs. In the third round on new
> year's night, Dex and Paul dared to take a bet, and won. Allow me to cite
> from their final email exchange on Dec 31st:
>
> Dex:
> Want to test the limits?
>
> Paul:
> Yes please.
> Let's go for broke.
> 8 seconds is close to the limit, which is what I'd like to see.
>
>
> The ultimate goal of this work has been to take decoding sensitivity close
> to the theroretical limit. An universal metric for this is Eb/N0, the ratio
> of the received signal energy per payload bit (Eb in Joules) and the noise
> spectral power density (N0 in Watt/Hertz, equivalent to "noise energy" in
> Joules). The Shannon limit for long messages spread to infinite bandwidth
> is
>  Eb/N0 = ln(2) = -1.59 dB,
> which (similar to the speed of light) cannot be surpassed by any possible
> encoding scheme. Paul's and Dex' experiments showed that his codes can come
> within about a dB of this limit in a real long-distance propagation
> experiment.
>
> To put that into perspective, let's derive Eb/N0 figures for two popular
> digital modes:
>
> WSPR-15 transmits 50 information bits in 15 minutes, ie one bit in 18
> seconds. The decoding threshold is -38 dB in 2.5 kHz, or -4 dBHz. This
> gives
>  Eb/N0 = 10 log(18) - 4 dB = +8.5 dB,
> ie. about 10 dB above the Shannon limit. Note that although different
> speed variants (eg WSPR-2) need different power, the minimum energy per bit
> has to remain the same.
>
> Opera-32 carries 28 information bits in 32.6 minutes, ie. one bit in 70
> seconds. The threshold is about -39.5 dB in 2.5 kHz, (-5.5 dBHz),
> referenced to the average power of the 50% dutycycle on-off keying. This
> gives
>  Eb/N0 = 10 log(70) - 5.5 dB = +13 dB
> or about 14.5 dB above Shannon. Note however that for LF / VLF
> transmissions, the limit will often be antenna voltage and peak power
> rather than average power, which can result in a further 3 dB disadvantage
> for Opera against frequency- or phase-modulated techniques.
>
> The opds correlation decoder can go about 9 dB lower than Opera. But of
> course it can only find the best match from an a-priori defined list of
> callsigns, and doesn't attempt to decode any message.
>
> However we must recognize that the amateur modes spend a significant part
> of their energy to provide a reference for synchronisation, so not all of
> the Eb/N0 difference is due to less efficient encoding. The "nude" FEC-PSK
> mode doesn't contain any such overhead. So it can only work when the link
> has a stable phase (like on VLF), and the decoder has been given accurate
> information on carrier frequency and symbol timing.
>
> All the best,
> Markus (DF6NM)
>
>  *From:* Paul Nicholson <vlf0403@abelian.org>
> *Sent:* Sunday, January 04, 2015 1:13 PM
> *To:* rsgb_lf_group@blacksheep.org
> *Subject:* VLF: Transatlantic messages at 8822Hz
>
>
> W4DEX achieved another 'first' recently by sending a series of
> messages across the Atlantic at 8822 Hz which were successfully
> copied at Todmorden UK, range 6194km.
>
> Transmissions used coherent BPSK signalling with ERP of around
> 150uW.   The modulation encoded the messages using a rate
> 1/16 terminated convolutional code with constraint length 25,
> cascaded with an outer error detection code.
>
> The first message was received at 2014-12-30 03:00, a 4
> character message 'EM95'.  Eb/N0 was -0.8dB using 9 second
> symbols.
>
> A second test the following night managed 12 characters 'PAUL
> HNY DEX' using 14 second symbols giving Eb/N0 of +1.0dB.
> Conditions were good and we could have used shorter symbols
> and a longer message.
>
> The third test and best result so far was a 25 character message
> '8822HZ 2015 JAN 1 TA TEST' sent from 2015-01-01 00:00 using
> 8 second symbols.  This was received with Eb/N0 = -0.1dB.
>
> In the 0.125 Hz bandwidth of a code symbol, the S/N was -13.2dB.
> That corresponds to -56dB S/N in a 2.5kHz audio bandwidth
> after sferic blanking.  Before the blanker the S/N would be
> around -76dB.
>
> The source encoding uses 6 bits per character to produce a
> payload of 150 bits.  An outer code adds a 16 bit CRC and the
> convolutional encoder expands the message to 3040 signal bits.
> The effective code rate is therefore 150/3040 = 1/20.27.
>
> Of the 3040 signal bits, 1153 were demodulated incorrectly
> but the FEC was able to fix them all to reveal the message.
>
> Received signal was around 0.12 fT and it was necessary to
> combine H-field and E-field receiver outputs to obtain a
> sufficient S/N to decode.
>
> The decoder is a soft Viterbi list decoder.  The signals are too
> weak to reveal a reference phase by the usual method of summing
> the squared complex symbol amplitudes.  Instead the decoder has
> to do a brute force trial and error search.
>
> The information rate in the 3rd test was 24.6 bits per hour
> which is 80% of the channel capacity.
>
> --
> Paul Nicholson
> http://abelian.org/
> --
>
>


-- 
73 Warren K2ORS
                WD2XGJ
                WD2XSH/23
                WE2XEB/2
                WE2XGR/1

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<div dir=3D"ltr"><div>Paul, Dex, Markus,</div><div>=C2=A0</div><div>=C2=A0=
=C2=A0=C2=A0=C2=A0 First congratulations Dex and Paul !</div><div>=C2=A0</d=
iv><div>Second, it has been many years since my graduate work in mathematic=
s at Courant, and then it was oriented toward PDE&#39;s, fluid mechanics, c=
omplex variable, and mathematical methods.=C2=A0 </div><div>What is the bes=
t text for getting up to speed on convolutional coding and Viterbi decoding=
?</div><div>=C2=A0</div><div>73 &amp; tnx Warren</div><div>=C2=A0</div><div=
>=C2=A0</div><div>=C2=A0</div><div><span dir=3D"auto"></span>=C2=A0</div></=
div><div class=3D"gmail_extra"><br><div class=3D"gmail_quote">On Sun, Jan 4=
, 2015 at 10:11 AM, Markus Vester <span dir=3D"ltr">&lt;<a href=3D"mailto:m=
arkusvester@aol.com" target=3D"_blank">markusvester@aol.com</a>&gt;</span> =
wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;bord=
er-left:1px #ccc solid;padding-left:1ex"><u></u>


<div style=3D"padding-top:15px;padding-right:10px;padding-left:10px" name=
=3D"Compose message area" bgcolor=3D"#ffffff">
<div><font face=3D"Arial">Big congratulations again to Paul and Dex!=20
</font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">What Paul described in unpretentious and=20
matter-of-fact words should really be regarded as a major achievement. It h=
as=20
been a well-deserved fruit of several months of effort, and there were a nu=
mber=20
of difficulties to be overcome. As I was lucky to be included in the preced=
ing=20
email exchange, I had the chance to witness milestones and setbacks during =
the=20
process. </font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">Most members of the LF group will appreciate the=
=20
challenges to Dex on the sub-9kHz transmit side, dealing with large coils a=
nd=20
high voltage, realizing accurate GPS-derived frequencies and sub-second bit=
=20
timing, and last not least being able to leave the signal on air reliably f=
or=20
many hours. </font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">The information processing side handled solely by=
=20
Paul surely presented an even higher hurdle: In the first place, he searche=
d and=20
found a small handful of &quot;good&quot; FEC codes. The search involved ex=
tensive=20
simulations on powerful multicore computers hired from the Amazon cloud. Th=
en=20
the soft Viterby decoding of a potential receive signal is also computer=20
intensive, especially for longer messages. There need to be numerous trials=
=20
while optimising reference phase evolution, bit timing, and antenna=20
weights.</font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">Perhaps the most challenging part was guessing=20
appropriate parameters before a transmission, ie. how many characters shoul=
d be=20
sent in which amount of time. Although some experience had been gained from=
=20
carrier measurements during previous nights, ionospheric and atmospheric=20
variations make it hard to predict SNR accurately enough if you want to exp=
loit=20
the channel capacity to the last couple of dBs. In the third round on new y=
ear&#39;s=20
night, Dex and Paul dared to take a bet, and won. Allow me to cite from the=
ir=20
final email exchange on Dec 31st:</font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">Dex:<br>Want to test the limits?</font></div>
<div><font face=3D"Arial"></font>=C2=A0</div>
<div><font face=3D"Arial">Paul: <br>Yes please. <br>Let&#39;s go for broke.=
 <br>8=20
seconds is close to the limit, which is what I&#39;d like to see. </font></=
div>
<div><font face=3D"Arial"></font>=C2=A0</div><font face=3D"Arial">
<div><br>The ultimate goal of this work has been to take decoding sensitivi=
ty=20
close to the theroretical limit. An universal metric for this is Eb/N0, the=
=20
ratio of the received signal energy per payload bit (Eb in Joules) and the =
noise=20
spectral power density (N0 in Watt/Hertz, equivalent to &quot;noise energy&=
quot; in=20
Joules). The Shannon limit for long messages spread to infinite bandwidth i=
s=20
<br>=C2=A0Eb/N0 =3D ln(2) =3D -1.59 dB, <br>which (similar to the speed of =
light)=20
cannot be surpassed by any possible encoding scheme. Paul&#39;s and Dex&#39=
; experiments=20
showed that his codes can come within about a dB of this limit in a real=20
long-distance propagation experiment. </div>
<div>=C2=A0</div>
<div>To put that into perspective, let&#39;s derive Eb/N0 figures for two p=
opular=20
digital modes:</div>
<div>=C2=A0</div>
<div>WSPR-15 transmits 50 information bits in 15 minutes, ie one bit in 18=
=20
seconds. The decoding threshold is -38 dB in 2.5 kHz, or -4 dBHz. This give=
s=20
<br>=C2=A0Eb/N0 =3D 10 log(18) - 4 dB =3D +8.5 dB,<br>ie. about 10 dB above=
 the=20
Shannon limit. Note that although different speed variants (eg WSPR-2) need=
=20
different power, the minimum energy per bit has to remain the same.</div>
<div>=C2=A0</div>
<div>Opera-32 carries 28 information bits in 32.6 minutes, ie. one bit in 7=
0=20
seconds. The threshold is about -39.5 dB in 2.5 kHz, (-5.5 dBHz), reference=
d to=20
the average power of the 50% dutycycle on-off keying. This gives<br>=C2=A0E=
b/N0=20
=3D 10 log(70) - 5.5 dB =3D +13 dB<br>or about 14.5 dB above Shannon. Note =
however=20
that for LF / VLF transmissions, the limit will often be antenna voltage an=
d=20
peak power rather than average power, which can result in a further 3 dB=20
disadvantage for Opera against frequency- or phase-modulated=20
techniques.=C2=A0=C2=A0 </div>
<div>=C2=A0</div>
<div>The opds correlation decoder can go about 9 dB lower than Opera. But o=
f=20
course it can only find the best match from an a-priori defined list of=20
callsigns, and doesn&#39;t attempt to decode any message.</div>
<div>=C2=A0</div>
<div>However we must recognize that the amateur modes spend a significant p=
art=20
of their energy to provide a reference for synchronisation, so not all of t=
he=20
Eb/N0 difference is due to less efficient encoding. The &quot;nude&quot; FE=
C-PSK mode=20
doesn&#39;t contain any such overhead. So it can only work when the link ha=
s a=20
stable phase (like on VLF), and the decoder has been given accurate informa=
tion=20
on carrier frequency and symbol timing.</div>
<div>=C2=A0</div>
<div>All the best,<br>Markus (DF6NM)=C2=A0 <br></div></font></div>
<div style=3D"font:10pt/normal Tahoma;font-size-adjust:none;font-stretch:no=
rmal">
<div><br></div>
<div style=3D"background:rgb(245,245,245)">
<div><b>From:</b> <a title=3D"vlf0403@abelian.org" href=3D"mailto:vlf0403@a=
belian.org" target=3D"_blank">Paul Nicholson</a> </div>
<div><b>Sent:</b> Sunday, January 04, 2015 1:13 PM</div>
<div><b>To:</b> <a title=3D"rsgb_lf_group@blacksheep.org" href=3D"mailto:rs=
gb_lf_group@blacksheep.org" target=3D"_blank">rsgb_lf_group@blacksheep.org<=
/a>=20
</div>
<div><b>Subject:</b> VLF: Transatlantic messages at 8822Hz</div></div></div=
><div class=3D"HOEnZb"><div class=3D"h5">
<div><br></div><br>W4DEX achieved another &#39;first&#39; recently by sendi=
ng a series=20
of<br>messages across the Atlantic at 8822 Hz which were successfully<br>co=
pied=20
at Todmorden UK, range 6194km.<br><br>Transmissions used coherent BPSK=20
signalling with ERP of around<br>150uW.=C2=A0=C2=A0 The modulation encoded =
the=20
messages using a rate<br>1/16 terminated convolutional code with constraint=
=20
length 25,<br>cascaded with an outer error detection code.<br><br>The first=
=20
message was received at 2014-12-30 03:00, a 4<br>character message &#39;EM9=
5&#39;.=C2=A0=20
Eb/N0 was -0.8dB using 9 second<br>symbols.<br><br>A second test the follow=
ing=20
night managed 12 characters &#39;PAUL<br>HNY DEX&#39; using 14 second symbo=
ls giving=20
Eb/N0 of +1.0dB.<br>Conditions were good and we could have used shorter=20
symbols<br>and a longer message.<br><br>The third test and best result so f=
ar=20
was a 25 character message<br>&#39;8822HZ 2015 JAN 1 TA TEST&#39; sent from=
 2015-01-01=20
00:00 using<br>8 second symbols.=C2=A0 This was received with Eb/N0 =3D=20
-0.1dB.<br><br>In the 0.125 Hz bandwidth of a code symbol, the S/N was=20
-13.2dB.<br>That corresponds to -56dB S/N in a 2.5kHz audio bandwidth<br>af=
ter=20
sferic blanking.=C2=A0 Before the blanker the S/N would be<br>around=20
-76dB.<br><br>The source encoding uses 6 bits per character to produce=20
a<br>payload of 150 bits.=C2=A0 An outer code adds a 16 bit CRC and=20
the<br>convolutional encoder expands the message to 3040 signal bits.<br>Th=
e=20
effective code rate is therefore 150/3040 =3D 1/20.27.<br><br>Of the 3040 s=
ignal=20
bits, 1153 were demodulated incorrectly<br>but the FEC was able to fix them=
 all=20
to reveal the message.<br><br>Received signal was around 0.12 fT and it was=
=20
necessary to<br>combine H-field and E-field receiver outputs to obtain=20
a<br>sufficient S/N to decode.<br><br>The decoder is a soft Viterbi list=20
decoder.=C2=A0 The signals are too<br>weak to reveal a reference phase by t=
he=20
usual method of summing<br>the squared complex symbol amplitudes.=C2=A0 Ins=
tead=20
the decoder has<br>to do a brute force trial and error search.<br><br>The=
=20
information rate in the 3rd test was 24.6 bits per hour<br>which is 80% of =
the=20
channel capacity.<br><br>--<br>Paul Nicholson<br><a href=3D"http://abelian.=
org/" target=3D"_blank">http://abelian.org/</a><br>--<br><br>
</div></div></blockquote></div><br><br clear=3D"all"><br>-- <br><div class=
=3D"gmail_signature">73 Warren K2ORS<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 WD2XGJ <br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 WD2XSH/23<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 WE2XEB/2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 WE2XGR/1<br><br>=C2=A0</div>
</div>

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