Experiment: Deep Learning algorithm for Morse decoder using LSTM RNN

INTRODUCTION

In my previous post I created a Python script to generate training material for neural networks.
The goal is to test how well the modern Deep Learning algorithms would work in decoding noisy Morse signals with heavy QSB fading.

I did some research on various frameworks and found this article  from Daniel Hnyk. My requirements were quite similar - full Python support, LSTM RNN built-in and a simple interface.
He had selected Keras that is available in Github. There is a mailing list for Keras users that is fairly active and quite useful to find support from other users. I installed Keras on my Linux laptop and using Jupyter interactive notebooks it was easy to start experimenting with various neural network configurations.

SIMPLE RECURRENT NEURAL NETWORK EXPERIMENT

Using various sources and above mailing list I came up with the following experiment. I have uploaded the Jupyter notebook file in Github in case the reader wants to replicate the experiment.

The source code or printed output text is shown below with courier font  and I have added some commentary as well as the graphs as pictures.


In [12]:
#!/usr/bin/env python
# MorseEncoder.py  - Morse Encoder to generate training material for neural networks
# Generates raw signal waveforms with Gaussian noise and QSB (signal fading) effects
# Provides also the training target variables in separate columns. Example usage:
#
# WPM= 40 # speed 40 words per minute
# Tq = 4. # QSB cycle time in seconds (typically 5..10 secs)
# sigma = 0.02 # add some Gaussian noise
# P = signal('QUICK BROWN FOX JUMPED OVER THE LAZY FOX ',WPM,Tq,sigma)
# from matplotlib.pyplot import  plot,show,figure,legend
# from numpy.random import normal
# figure(figsize=(12,3))
# lb1,=plot(P.t,P.sig,'b',label="sig")
# lb2,=plot(P.t,P.dit,'g',label="dit")
# lb3,=plot(P.t,P.dah,'g',label="dah")
# lb4,=plot(P.t,P.ele,'m',label="ele")
# lb5,=plot(P.t,P.chr,'c',label="chr")
# lb6,=plot(P.t,P.wrd,'r*',label="wrd")
# legend([lb1,lb2,lb3,lb4,lb5,lb6])
# show()
# P.to_csv("MorseTest.csv")
#
# Copyright (C) 2015   Mauri Niininen, AG1LE
#
#
# MorseEncoder.py is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# MorseEncoder.py is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with bmorse.py.  If not, see <http://www.gnu.org/licenses/>.

import numpy as np
import pandas as pd
from numpy import sin,pi
from numpy.random import normal
pd.options.mode.chained_assignment = None  #to prevent warning messages

Morsecode = {
 '!': '-.-.--',
 '$': '...-..-',
 "'": '.----.',
 '(': '-.--.',
 ')': '-.--.-',
 ',': '--..--',
 '-': '-....-',
 '.': '.-.-.-',
 '/': '-..-.',
 '0': '-----',
 '1': '.----',
 '2': '..---',
 '3': '...--',
 '4': '....-',
 '5': '.....',
 '6': '-....',
 '7': '--...',
 '8': '---..',
 '9': '----.',
 ':': '---...',
 ';': '-.-.-.',
 '<AR>': '.-.-.',
 '<AS>': '.-...',
 '<HM>': '....--',
 '<INT>': '..-.-',
 '<SK>': '...-.-',
 '<VE>': '...-.',
 '=': '-...-',
 '?': '..--..',
 '@': '.--.-.',
 'A': '.-',
 'B': '-...',
 'C': '-.-.',
 'D': '-..',
 'E': '.',
 'F': '..-.',
 'G': '--.',
 'H': '....',
 'I': '..',
 'J': '.---',
 'K': '-.-',
 'L': '.-..',
 'M': '--',
 'N': '-.',
 'O': '---',
 'P': '.--.',
 'Q': '--.-',
 'R': '.-.',
 'S': '...',
 'T': '-',
 'U': '..-',
 'V': '...-',
 'W': '.--',
 'X': '-..-',
 'Y': '-.--',
 'Z': '--..',
 '\\': '.-..-.',
 '_': '..--.-',
 '~': '.-.-'}
    

def encode_morse(cws):
    s=[]
    for chr in cws:
        try: # try to find CW sequence from Codebook
            s += Morsecode[chr]
            s += ' '
        except:
            if chr == ' ':
                s += '_'
                continue
            print "error: '%s' not in Codebook" % chr
    return ''.join(s)



def len_dits(cws):
    # length of string in dit units, include spaces
    val = 0
    for ch in cws:
        if ch == '.': # dit len + el space 
            val += 2
        if ch == '-': # dah len + el space
            val += 4
        if ch==' ':   #  el space
            val += 2
        if ch=='_':   #  el space
            val += 7
    return val


def signal(cw_str,WPM,Tq,sigma):
    # for given CW string i.e. 'ABC ' 
    # return a pandas dataframe with signals and  symbol probabilities
    # WPM = Morse speed in Words Per Minute (typically 5...50)
    # Tq  = QSB cycle time (typically 3...10 seconds) 
    # sigma = adds gaussian noise with standard deviation of sigma to signal
    cws = encode_morse(cw_str)
    #print cws
    # calculate how many milliseconds this string will take at speed WPM
    ditlen = 1200/WPM # dit length in msec, given WPM
    msec = ditlen*(len_dits(cws)+7)  # reserve +7 for the last pause
    t = np.arange(msec)/ 1000.       # time array in seconds
    ix = range(0,msec)               # index for arrays

    # Create a DataFrame and initialize
    col =["t","sig","dit","dah","ele","chr","wrd","spd"]
    P = pd.DataFrame(index=ix,columns=col)
    P.t = t              # keep time  
    P.sig=np.zeros(msec) # signal stored here
    P.dit=np.zeros(msec) # probability of 'dit' stored here
    P.dah=np.zeros(msec) # probability of 'dah' stored here
    P.ele=np.zeros(msec) # probability of 'element space' stored here
    P.chr=np.zeros(msec) # probability of 'character space' stored here
    P.wrd=np.zeros(msec) # probability of 'word space' stored here
    P.spd=np.ones(msec)*WPM #speed stored here 

    
    #pre-made arrays with multiple(s) of ditlen
    z = np.zeros(ditlen) 
    z2 = np.zeros(2*ditlen)
    z4 = np.zeros(4*ditlen)
    dit = np.ones(ditlen)
    dah = np.ones(3*ditlen)
      
    # For all dits/dahs in CW string generate the signal, update symbol probabilities
    i = 0
    for ch in cws:
        if ch == '.':
            dur = len(dit)
            P.sig[i:i+dur] = dit
            P.dit[i:i+dur] = dit
            i += dur
            dur=len(z)
            P.sig[i:i+dur] = z
            P.ele[i:i+dur] = np.ones(dur)
            i += dur

        if ch == '-':
            dur = len(dah)
            P.sig[i:i+dur] = dah
            P.dah[i:i+dur]=  dah
            i += dur            
            dur=len(z)
            P.sig[i:i+dur] = z
            P.ele[i:i+dur] = np.ones(dur)
            i += dur

        if ch == ' ':
            dur = len(z2)
            P.sig[i:i+dur] = z2
            P.chr[i:i+dur]=  np.ones(dur)
            i += dur
        if ch == '_':
            dur = len(z4)
            P.sig[i:i+dur] = z4
            P.wrd[i:i+dur]=  np.ones(dur)
            i += dur
    if Tq > 0.:  # QSB cycle time impacts signal amplitude
        qsb = 0.5 * sin((1./float(Tq))*t*2*pi) +0.55
        P.sig = qsb*P.sig
    if sigma >0.:
        P.sig += normal(0,sigma,len(P.sig))
    return P
In [13]:
print ('MorseEncoder started')
%matplotlib inline
from matplotlib.pyplot import  plot,show,figure,legend, title
from numpy.random import normal
WPM= 40
Tq = 1.8 # QSB cycle time in seconds (typically 5..10 secs)
sigma = 0.01 # add some Gaussian noise
P = signal('QUICK',WPM,Tq,sigma)
figure(figsize=(12,3))
lb1,=plot(P.t,P.sig,'b',label="sig")
title("QUICK in Morse code - (c) 2015 AG1LE")
legend([lb1])
show()
print ('MorseEncoder finished. %d datapoints created' % len(P.sig)) 

MorseEncoder started

The Jupyter notebook will plot this graph that basically shows the text 'QUICK' converted to noisy signal with strong QSB fading.  This signal goes down close to zero between letters C and K as you can see below.  

Figure 1.  The training signal containing noise and QSB fading

The next  section of the code imports some libraries (including Keras) that is used for Neural Network experimentation. I am also preparing the data to the proper format that Keras requires. 


MorseEncoder finished. 1950 datapoints created
In [14]:
# Time Series Testing - Morse case
import keras.callbacks
from keras.models import Sequential  
from keras.layers.core import Dense, Activation, Dense, Dropout
from keras.layers.recurrent import LSTM

import random
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

# Data preparation 
# use 100 examples of data to predict nb_samples (850) in the future
samples = 1950
examples = 1000
y_examples = 100

x = np.linspace(0,1950,samples)
nb_samples = samples - examples - y_examples
data = P.sig

# prepare input for RNN training  - 1 feature
input_list = [np.expand_dims(np.atleast_2d(data[i:examples+i]), axis=0) for i in xrange(nb_samples)]
input_mat = np.concatenate(input_list, axis=0)
lb1,=plot(x,data,label="input")
lb2,=plot(x,P.dit,label="target")
legend([lb1,lb2])
title("training input and target data")
Out[14]:
<matplotlib.text.Text at 0x10c119b50>


This graph shows the training data (the noisy, fading signal) and the target data (I selected 'dits' in this example). This is just to verify that I have the right datasets selected. 

Figure 2.  Training and target data 

In the following sections I prepare the training target ('dits') to proper format and setup the neural network model.  I am using LSTM with Dropout and the model has 300 hidden neurons.  I have also a callback function defined to capture the loss data during the training so that I can plot the loss curve to see the training progress.  

In [15]:
# prepare target - the first column in merged dataframe
ydata = P.dit
target_list = [np.atleast_2d(ydata[i+examples:examples+i+y_examples]) for i in xrange(nb_samples)]
target_mat = np.concatenate(target_list, axis=0)

# set up a model
trials = input_mat.shape[0]
features = input_mat.shape[2]
hidden = 300

model = Sequential()
model.add(LSTM(input_dim=features, output_dim=hidden,return_sequences=False))
model.add(Dropout(.2))
model.add(Dense(input_dim=hidden, output_dim=y_examples))
model.add(Activation('linear'))
model.compile(loss='mse', optimizer='rmsprop')

# Call back to capture losses 
class LossHistory(keras.callbacks.Callback):
    def on_train_begin(self, logs={}):
        self.losses = []

    def on_batch_end(self, batch, logs={}):
        self.losses.append(logs.get('loss'))
# Train the model
history = LossHistory()
model.fit(input_mat, target_mat, nb_epoch=100,callbacks=[history])

# Plot the loss curve 
plt.plot( history.losses)
title("training loss")

Here I have started the training. I selected 100 epochs - this means that the software will go through the training material  for 100 times during the training.  As you can see this goes very quickly - with larger model or larger datasets the training might take minutes to hours per epoch. We have a very small model and small dataset here. 

Epoch 1/100
850/850 [==============================] - 0s - loss: 0.1050     
Epoch 2/100
850/850 [==============================] - 0s - loss: 0.0927     
Epoch 3/100
850/850 [==============================] - 0s - loss: 0.0870     
Epoch 4/100
850/850 [==============================] - 0s - loss: 0.0823     
Epoch 5/100
850/850 [==============================] - 0s - loss: 0.0788     
Epoch 6/100
850/850 [==============================] - 0s - loss: 0.0756     
Epoch 7/100
850/850 [==============================] - 0s - loss: 0.0724     
Epoch 8/100
850/850 [==============================] - 0s - loss: 0.0693     
Epoch 9/100
850/850 [==============================] - 0s - loss: 0.0668     
Epoch 10/100
850/850 [==============================] - 0s - loss: 0.0639     
Epoch 11/100
850/850 [==============================] - 0s - loss: 0.0611     
Epoch 12/100
850/850 [==============================] - 0s - loss: 0.0586     
Epoch 13/100
850/850 [==============================] - 0s - loss: 0.0561     
Epoch 14/100
850/850 [==============================] - 0s - loss: 0.0539     
Epoch 15/100
850/850 [==============================] - 0s - loss: 0.0519     
Epoch 16/100
850/850 [==============================] - 0s - loss: 0.0495     
Epoch 17/100
850/850 [==============================] - 0s - loss: 0.0476     
Epoch 18/100
850/850 [==============================] - 0s - loss: 0.0456     
Epoch 19/100
850/850 [==============================] - 0s - loss: 0.0441     
Epoch 20/100
850/850 [==============================] - 0s - loss: 0.0430     
Epoch 21/100
850/850 [==============================] - 0s - loss: 0.0411     
Epoch 22/100
850/850 [==============================] - 0s - loss: 0.0400     
Epoch 23/100
850/850 [==============================] - 0s - loss: 0.0387     
Epoch 24/100
850/850 [==============================] - 0s - loss: 0.0378     
Epoch 25/100
850/850 [==============================] - 0s - loss: 0.0370     
Epoch 26/100
850/850 [==============================] - 0s - loss: 0.0356     
Epoch 27/100
850/850 [==============================] - 0s - loss: 0.0350     
Epoch 28/100
850/850 [==============================] - 0s - loss: 0.0340     
Epoch 29/100
850/850 [==============================] - 0s - loss: 0.0334     
Epoch 30/100
850/850 [==============================] - 0s - loss: 0.0328     
Epoch 31/100
850/850 [==============================] - 0s - loss: 0.0322     
Epoch 32/100
850/850 [==============================] - 0s - loss: 0.0317     
Epoch 33/100
850/850 [==============================] - 0s - loss: 0.0309     
Epoch 34/100
850/850 [==============================] - 0s - loss: 0.0302     
Epoch 35/100
850/850 [==============================] - 0s - loss: 0.0299     
Epoch 36/100
850/850 [==============================] - 0s - loss: 0.0296     
Epoch 37/100
850/850 [==============================] - 0s - loss: 0.0290     
Epoch 38/100
850/850 [==============================] - 0s - loss: 0.0285     
Epoch 39/100
850/850 [==============================] - 0s - loss: 0.0283     
Epoch 40/100
850/850 [==============================] - 0s - loss: 0.0277     
Epoch 41/100
850/850 [==============================] - 0s - loss: 0.0272     
Epoch 42/100
850/850 [==============================] - 0s - loss: 0.0268     
Epoch 43/100
850/850 [==============================] - 0s - loss: 0.0265     
Epoch 44/100
850/850 [==============================] - 0s - loss: 0.0258     
Epoch 45/100
850/850 [==============================] - 0s - loss: 0.0256     
Epoch 46/100
850/850 [==============================] - 0s - loss: 0.0253     
Epoch 47/100
850/850 [==============================] - 0s - loss: 0.0251     
Epoch 48/100
850/850 [==============================] - 0s - loss: 0.0248     
Epoch 49/100
850/850 [==============================] - 0s - loss: 0.0246     
Epoch 50/100
850/850 [==============================] - 0s - loss: 0.0241     
Epoch 51/100
850/850 [==============================] - 0s - loss: 0.0236     
Epoch 52/100
850/850 [==============================] - 0s - loss: 0.0233     
Epoch 53/100
850/850 [==============================] - 0s - loss: 0.0234     
Epoch 54/100
850/850 [==============================] - 0s - loss: 0.0230     
Epoch 55/100
850/850 [==============================] - 0s - loss: 0.0229     
Epoch 56/100
850/850 [==============================] - 0s - loss: 0.0224     
Epoch 57/100
850/850 [==============================] - 0s - loss: 0.0223     
Epoch 58/100
850/850 [==============================] - 0s - loss: 0.0218     
Epoch 59/100
850/850 [==============================] - 0s - loss: 0.0218     
Epoch 60/100
850/850 [==============================] - 0s - loss: 0.0215     
Epoch 61/100
850/850 [==============================] - 0s - loss: 0.0215     
Epoch 62/100
850/850 [==============================] - 0s - loss: 0.0212     
Epoch 63/100
850/850 [==============================] - 0s - loss: 0.0208     
Epoch 64/100
850/850 [==============================] - 0s - loss: 0.0209     
Epoch 65/100
850/850 [==============================] - 0s - loss: 0.0207     
Epoch 66/100
850/850 [==============================] - 0s - loss: 0.0205     
Epoch 67/100
850/850 [==============================] - 0s - loss: 0.0203     
Epoch 68/100
850/850 [==============================] - 0s - loss: 0.0200     
Epoch 69/100
850/850 [==============================] - 0s - loss: 0.0200     
Epoch 70/100
850/850 [==============================] - 0s - loss: 0.0197     
Epoch 71/100
850/850 [==============================] - 0s - loss: 0.0197     
Epoch 72/100
850/850 [==============================] - 0s - loss: 0.0198     
Epoch 73/100
850/850 [==============================] - 0s - loss: 0.0193     
Epoch 74/100
850/850 [==============================] - 0s - loss: 0.0191     
Epoch 75/100
850/850 [==============================] - 0s - loss: 0.0189     
Epoch 76/100
850/850 [==============================] - 0s - loss: 0.0188     
Epoch 77/100
850/850 [==============================] - 0s - loss: 0.0189     
Epoch 78/100
850/850 [==============================] - 0s - loss: 0.0185     
Epoch 79/100
850/850 [==============================] - 0s - loss: 0.0185     
Epoch 80/100
850/850 [==============================] - 0s - loss: 0.0184     
Epoch 81/100
850/850 [==============================] - 0s - loss: 0.0183     
Epoch 82/100
850/850 [==============================] - 0s - loss: 0.0181     
Epoch 83/100
850/850 [==============================] - 0s - loss: 0.0180     
Epoch 84/100
850/850 [==============================] - 0s - loss: 0.0179     
Epoch 85/100
850/850 [==============================] - 0s - loss: 0.0177     
Epoch 86/100
850/850 [==============================] - 0s - loss: 0.0177     
Epoch 87/100
850/850 [==============================] - 0s - loss: 0.0174     
Epoch 88/100
850/850 [==============================] - 0s - loss: 0.0177     
Epoch 89/100
850/850 [==============================] - 0s - loss: 0.0175     
Epoch 90/100
850/850 [==============================] - 0s - loss: 0.0173     
Epoch 91/100
850/850 [==============================] - 0s - loss: 0.0172     
Epoch 92/100
850/850 [==============================] - 0s - loss: 0.0171     
Epoch 93/100
850/850 [==============================] - 0s - loss: 0.0171     
Epoch 94/100
850/850 [==============================] - 0s - loss: 0.0167     
Epoch 95/100
850/850 [==============================] - 0s - loss: 0.0167     
Epoch 96/100
850/850 [==============================] - 0s - loss: 0.0170     
Epoch 97/100
850/850 [==============================] - 0s - loss: 0.0164     
Epoch 98/100
850/850 [==============================] - 0s - loss: 0.0166     
Epoch 99/100
850/850 [==============================] - 0s - loss: 0.0163     
Epoch 100/100
850/850 [==============================] - 0s - loss: 0.0164     
Out[15]:
<matplotlib.text.Text at 0x11e055350>

The following graph shows the training loss during the training process. This gives you an idea whether the training is progressing well or if you have some problem with the model or the parameters. 

Figure 3.  Training loss curve

In [16]:
# Use training data to check prediction
predicted = model.predict(input_mat)
In [17]:
# Plot original data (green) and predicted data (red)
lb1,=plot(data,'g',label="training")
#lb2,=plot(ydata,'b',label="target")
lb3,=plot(xrange(examples,examples+nb_samples), predicted[:,1],'r',label="predicted")
legend([lb1,lb3])
title("training vs. predicted")
Out[17]:
<matplotlib.text.Text at 0x11f164610>

In this section I am checking the model prediction. Since I am using the training material this is supposed to show a good result if the training was successful.  As you can see from figure 4. below the predicted graph (red color)  is aligned with 'dits' in the training signal (green color) despite QSB fading and noise in the signal.  

Figure 4.  Training vs. predicted graph

In the following section I will create another Morse signal, this time with text 'KCIUQ' but using the same noise, QSB and speed parameters.  I am planning to use this signal to validate how well the model has generalized the 'dit' concept.  

In [18]:
# Let's change the input signal, instead of QUICK we have KCIUQ in Morse code 
P = signal('KCIUQ',WPM,Tq,sigma)
data = P.sig

# prepare input - 1 feature
input_list = [np.expand_dims(np.atleast_2d(data[i:examples+i]), axis=0) for i in xrange(nb_samples)]
input_mat = np.concatenate(input_list, axis=0)
plt.plot(x,data)
Out[18]:
[<matplotlib.lines.Line2D at 0x136050f90>]

Here is the generated validation Morse signal.  It has the same letter as before but in reverse order. Can you read letters 'KCIUQ' from the graph below?

Figure 5.  Validation Morse signal

In this section I use the above validation signal to create a prediction and the plot the results.  

In [19]:
predicted = model.predict(input_mat)
plt.plot(data,'g')
plt.plot(xrange(examples,examples+nb_samples), predicted[:,1],'r')
Out[19]:
[<matplotlib.lines.Line2D at 0x1217be9d0>]

As you can see from the graph below the predicted 'dit' symbols (red color)  don't really line up with actual 'dits' in the signal (green color). This is not a surprise to me.  To build a good model that can generalize the learning you need to have a lot of training material (typically millions of datapoints) and the model needs to have enough neural nodes to capture the details of the underlying signals.  
In this simple experiment I had only 1950 datapoints and 300 hidden nodes. There are only 8  'dit' symbols in the training material - learning CW skill  well requires a lot more material and many repetitions, as any human who has gone through the process can testify. Same principle applies for neural networks.  

Figure 6.  Validation test 

CONCLUSIONS 

In this experiment I built a proof of concept to test whether Recurrent Neural Networks (especially LSTM variant) could be used to learn to detect symbols from noisy Morse code that has deep QSB fading.  This experiment may contain errors and misunderstandings from my part as I have only had a few hours to play with this Keras Neural Network framework. Also, the concept itself needs still more validation as I may have used the framework incorrectly.

I think that the results look quite promising.  In only 100 epochs the RNN model learned 'dits' from the noisy signal and was able to separate them from 'dah' symbols.  As the validation test shows I overfitted the model to this small sample of training material used in the experiment.  It will take much more training data and larger, more complicated neural network to learn to generalize the symbols in Morse code.  The training process may also need more computing capacity. It might be beneficial to have a graphics card with GPU to speed up the training process going forward.

Any comments or feedback?

73
Mauri AG1LE