8822 Hz December 2014

8822 Hz - December 2014

25 Character BPSK message received by Paul Nicholson, Todmorden, UK

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 signaling 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/

31 December 2014

12 Character BPSK message received by Paul Nicholson, Todmorden, UK

From: Paul Nicholson
http://abelian.org/

Code rate 1/16 K=25
12 character message
14 second symbol period
Transmit 00:00 to 06:58:08

Message decoded straight away in Todmorden:

'PAUL HNY DEX'

Decode details:

crc OK rank 0: PAUL HNY DEX ps [ 0 0 0 0 0]
re-encode 674/1792 ber 3.76e-01 Es/N0=-13.0 Eb/N0=1.0 effrate=1/24.89

S/N was very good, about 2dB to spare. If only we'd known - we could
have gone for the 25 char message!

I'm now going to check some other sites - Sebring, Hawley,
and maybe even Bielefeld...

--
Paul Nicholson
--

31 December 2014 K3SIW Elgin, IL 634.2 miles-1020.6 km

(8842 Hz daylight carrier transmission)

30 December 2014

4 Character BPSK message received by Paul Nicholson, Todmorden, UK

by: Paul Nicholson
http://abelian.org/

Success at Todmorden on the 03:00 message from Dex.

Decoded 'EM95':

crc OK   rank 39: EM95 ps [    7 210 210 210 210]
re-encode 432/1024 ber 4.22e-01 Es/N0=-17.1 Eb/N0=-5.1 QD=16

The 210 210 210 210 thing is the reference phase for each
quarter of the message.

re-encode 432/1024 means that after successful decode, the
message is re-encoded and compared with what was received to
show we got 432 incorrectly demodulated signal bits out of the
1024 sent. The K=25 code was able to correct all these errors.

ber 4.22e-01 is the bit error rate which is just 432 / 1024.

Es/N0 is the S/N ratio in the bandwidth of a signal bit, 0.1Hz.

Eb/N0 is the S/N in the bandwidth of an information bit,
which for rate 1/16 is 1/16th the bandwidth of the signalling,
ie 6.25mHz.

In an audio bandwidth of say 2.5kHz, the message is 61dB below
the noise. That's after sferic blanking. About 80dB below
noise before the blanker.

rank 39 means that this was the 39th maximum likelihood
decode from the soft Viterbi list decoder. That means there
were 38 other decodes with fewer signalling errors, but they
all failed the CRC check in the outer error detection code.
(The decode list goes to 20,000 so 39 is very near the top).

Well, that's the most distant message ever sent by amateur
radio at VLF. First VLF T/A message. Also maybe the strongest
error correction code ever used by amateurs.

All four tests had, as far as I can tell, perfect timing of the
signal bits. An excellent transmission. I think conditions
weren't so good last night. With 9 second symbols the S/N
could have been 3 or 4dB better.

Perhaps the next test will try for a longer message?

Longer runs can be more robust.   The encoder scatters the
information bits and the error correction patterns around the
message and the decoder gathers them all up again. That means
that some badness at some part of the message, eg a drop-out
or phase wobble, can be compensated by an improvement elsewhere.

Eg a 2.5 hour transmission with a half-hour drop-out loses
20% of the signal bits.   The same drop-out in an 8 hour
transmission is only 6.3% of the bits.

I think the 00:00 transmission was probably hit by the phase
wobble we have seen on the carrier tests around 00:30 to 01:00.
There's good chance a longer test will ride that out and be
compensated by the improved S/N that often occurs later.

Am trying decode again of the 00:00 test using a wider range
of reference phase search.   Maybe I will also add in the
E-field to improve S/N slightly.

--
Paul Nicholson
http://abelian.org/