In the last blog post I evaluated FreeDV 700C over the air. This week I’ve been simulating the use of short LDPC FEC codes with Codec 2 700C over AWGN and HF channels.
In my HF Digital Voice work to date I have shied away from FEC:
- We didn’t have the bandwidth for the extra bits required for FEC.
- Modern, high performance codes tend to have large block sizes (1000’s of bits) which leads to large latency (several seconds) when applied to low bit rate speech.
- The error rates we are interested in (e.g. 10% raw, 1% after FEC decoder) are unusual – many codes don’t work well.
However with Codec 2 pushed down to 700 bit/s we now have enough bandwidth for a rate 1/2 code inside a standard 2kHz SSB channel. Over coffee a few weeks ago, Bill VK5DSP offered to develop some short LDPC codes for me specifically for this application. He sent me an Octave simulation of rate 1/2 and 2/3 codes of length 112 and 56 bits. Codec 2 700C has 28 bit frames so this corresponds to 4 or 2 Codec 2 700C frames, which would introduce a latencies of between 80 to 160ms – quite acceptable for Push To Talk (PTT) radio.
I re-factored Bill’s simulation code to produce ldpc_short.m. This measures BER and PER for Bill’s short LDPC codes, and also plots curves for theoretical, HF multipath channels, a Golay (24,12) code, and the current diversity scheme used in FreeDV 700C.
To check my results I compared the Golay BER and ideal HF multipath (Rayleigh Fading) channel curves to other peoples work. Always a good idea to spot check a few values and make sure they are sensible. I took a simple approach to get results in a reasonable amount of coding time (about 1 day of work in this case). This simulation runs at the symbol rate, and assumes ideal synchronisation. My other modem work (i.e experience) lets me move back and forth between this sort of simulation and real world modems, for example accounting for synchronisation losses.
Error Distribution and Packet Error Rate
I had an idea that Packet Error Rate (PER) might be important. Without FEC, bit errors are scattered randomly about. At our target 1% BER, many frames will have 1 or 2 bit errors. As discussed in the last post Codec 2 700C is sensitive to bit errors as “every bit counts”. For example one bit error in the Vector Quantiser (VQ) index (a big look up table) can throw the speech spectrum right off.
However a LDPC decoder will tend to correct all errors in a codeword, or “die trying” (i.e. fail badly). So an average output BER of say 1% will consist of a bunch of perfect frames, plus a completely trashed one every now and again. Digital voice works better with this style of error pattern than a few random errors in each codec packet. So for a given BER, a system that delivers a lower PER is better for our application. I’ve guesstimated a 10% PER target for intelligible low bit rate speech. Lets see how that works out…..
Here are the BER and PER curves for an AWGN channel:
Here are the same curves for HF (multipath fading) channel:
I’ve included a Golay (24,12) block code (hard decision) and uncoded PSK for comparison to the AWGN curves, and the diversity system on the HF curves. The HF channel is modelled as two paths with 1Hz Doppler spread and a 1ms delay.
The best LDPC code reaches the 1% BER/10% PER point at 2dB Eb/No (AWGN) and 6dB (HF multipath). Comparing BER, the coding gain is 2.5 and 3dB (AWGN and HF). Comparing PER, the coding gain is 3 and 5dB (AWGN and HF).
Here is a plot of the error pattern over time using the LDPC code on a HF channel at Eb/No of 6dB:
Note the errors are confined to short bursts – isolated packets where the decoder fails. Even though the average BER is 1%, most of the speech is error free. This is a very nice error distribution for digital speech.
Here are some speech samples, comparing the current diversity scheme used for FreeDV 700C to LDPC, for AWGN and LDPC channels. These were simulated by extracting the error pattern from the simulation then inserting these errors in a Codec 2 700C bit stream (see command lines section below).
|AWGN Eb/No 2dB||Diversity||LDPC|
|HF Eb/No 6dB||Diversity||LDPC|
These results are very encouraging and suggest a gain of 2 to 5dB over FreeDV 700C, and better error distribution (lower PER). Next step is to develop FreeDV 700D – a real world implementation using the 112 data-bit rate 1/2 LDPC code. This will require 4 frames of buffering, and some sort of synchronisation to determine the 112 bit frame boundaries. Fortunately much of the C code for these LDPC codes already exists, as it was developed for the Wenet High Altitude Balloon work.
If most frames at the decoder input are now error free, we can consider more efficient (but less robust) techniques for Codec 2, such as prediction (delta coding). This will decrease the codec bit rate for a given speech quality. We could then choose to reduce our bit rate (making the system more robust for a given channel SNR), or raise speech quality while maintaining the same bit rate.
Generating the decoded speech, first run the Octave ldpc_short simulation to generate “error pattern file”, then subject the Codec 2 700C bit stream to these error patterns.
octave:67> ldpc_short $ ./c2enc 700C ../../raw/ve9qrp_10s.raw - | ./insert_errors - - ../../octave/awgn_2dB_ldpc.err 28 | ./c2dec 700C - - | aplay -f S16_LE -
The simulation generate .eps files as direct generation of PNG leads to font size issues. Converting EPS to PNG without transparent background:
mogrify -resize 700x600 -density 300 -flatten -format png *.eps
However I still feel the images are a bit fuzzy, especially the text. Any ideas? Here’s the eps file if some one would like to try to get a nicer PNG conversion for me! The EPS file looks great at any scaling when I render it using the Ubuntu document viewer.
Update: A friend of mine (Erich) has suggested using GIMP for the conversion. This does seem to work well and has options for text and line anti-aliasing. It would be nice to be able to generate nice PNGs directly from Octave – my best approach so far is to capture screen shots.
LowSNR site Bill VK5DSP writes about his experiments in low SNR communications.
Wenet High Altitude Balloon SSDV System developed with Mark VK5QI and BIll VK5DSP that uses LDPC codes.