NEW BAYESIAN MORSE DECODERI have been working on a new Bayesian Morse decoder algorithm. This work is based on Dr. Bell's doctoral thesis that is one of the best and most comprehensive documents on this topic I have found so far. While it contains a lot of advanced mathematics this thesis has also very thorough description of the problems related to automatically transcribing the hand-keyed manual Morse signal with acceptable error rate. This thesis covers a lot of ground and describes with mathematical rigor how to model and solve each of the problems. It has also software examples (in Fortran) and test results comparing to theoretically optimal solution as well as to human performance under different conditions.
Using the thesis as a starting point I implemented the algorithms in C language. Current version has some 3335 lines of code and is posted in Github as open source with verbal permission from Dr. Bell. I managed to get the software working to the degree that I am able to run some performance tests. There is still a lot of work ahead to improve and clean up the code but I decided to publish some early results for those who might be interested in this work.
CORRELATOR-ESTIMATOR TESTINGAs described in the thesis this algorithm represents a "correlator-estimator" technique in which a sequence of all possible keystate transitions are hypothesized and correlated with the incoming signal, and the most likely sequence is output as the best estimate. To illustrate this point I plotted a segment of incoming signal with letters "QUICK B" as shown on figure 1. below. The probability estimates of various keystates [P(dit), P(dah), P(el-spc), P(chr-spc), P(wrd-spc), P(pause)] are plotted underneath the incoming signal. I used Kst Data Viewer to create this plot.
|Figure 1. Correlator-estimator probabilities
The Morse audio file used in this test had Signal-Noise Ratio (SNR) of 8 dB @ 2 kHz bandwidth. This figure shows nicely the time variant probability values of each keystate, as well as how a particular keystate correlates with "mark"/"space" changes in the incoming signal.
CER vs. SNR TESTINGTo test the decoder performance in the presence of noise I created a set of Morse sound files with -10 dB to +20 dB SNR @2kHz bandwidth using modified version of Rob Frohne KL7NA morse.m Octave software. These files contain 200 words with 5 random letters and numbers each. The sound files are available here: Morse sound files -10 dB ... 20dB SNR @2kHz BW For algorithm testing I also created corresponding text files where is each sample is a real number on separate line. These are easier to manipulate and plot using standard Linux tools, like gnuplot.
I ran the algorithm using files with different SNR levels and saved the decoder text output. To get the Character Error Rate (CER) I created a small utility program to calculate Levenshtein distance using this algorithm. Comparing original text to decoded text gives the character error rate. When plotting the results it was quite interesting to see a deep reduction in CER with SNR over 6 dB. Note that SNR figure contains noise for the whole 2kHz bandwidth.
|Figure 2. CER to SNR test results
The CER should go down to zero as SNR improves - however the graph shows some base error rate ~ 3 %. I need to study this a bit more in detail to find the root cause. At higher noise levels the curve shape looks a bit closer to what I expected.
NEXT STEPSAs mentioned before there is still a lot of work ahead to make this software useful.
I did some initial testing to integrate this decoder to a modified FLDIGI package and got the software partially working as an external program connected to FLDIGI via a Linux FIFO pipe.
I am also trying to figure out automated test scripts for timing and speed variance testing. I would really like to find the limits where the algorithm breaks. This requires more work in creating synthetic tests similar to what is described in the thesis.
Third area of work is testing the algorithm performance against signal fading. This would provide limits on real world signals and help to optimize the model parameters.
If you are interested in advancing the state of the art in Morse decoding feel free to download the software, work on testing & improving it. Please provide your feedback and post comments below.