In [1]:

    

import numpy as np


    

In [2]:

    

# probability of symbols
p = np.array( [ .25, .2, .2, .15, .07, .05, .025, .025, .02, .01] )
    
# get codeword lengths by rounding towards 0 and mapping to int
# (type conversion being necessary to use cw_lengths as indices)
cw_lengths = np.ceil( - np.log2( p ) )
cw_lengths = cw_lengths.astype( int )

# show probabilities and codewords lengths
print( 'Probabilities:' )
print( 'p = {}\n'.format( p ) )

print( 'Codeword lengths:' )
print( 'L(x_n) = {}'.format( cw_lengths ) )


    

    




Probabilities:
p = [ 0.25   0.2    0.2    0.15   0.07   0.05   0.025  0.025  0.02   0.01 ]

Codeword lengths:
L(x_n) = [2 3 3 3 4 5 6 6 6 7]

In [3]:

    

# function for determining the binary representation of a float
# using predefined number of fractional bits

def get_bin ( q, L):
    '''
    Multiplying by 2^L, rounding and transforming to bits
    '''

    q_up = int( q * 2**L )

    q_bin = np.binary_repr( q_up, width = L )
    
    return q_bin[ : L ]


    

In [4]:

    

# get cdf
# NOTE: 0 is pre-pended in order to realize Q_n = \sum_i=1^n-1 P(x_i)
F = np.cumsum( np.append( 0, p ) )

codewords = [ get_bin( F[ i ] , cw_lengths[ i ] ) for i in range( len( p ) ) ]

# printing
print('Codewords are:\n{}'.format( codewords ) )


    

    




Codewords are:
['00', '010', '011', '101', '1100', '11011', '111010', '111100', '111110', '1111110']

In [5]:

    

# Printing various information

print('Max. Entropie: \t\t\tH0 = {:2.3f}'.format( np.log2(len(p))) )

print('Entropy: \t\t\tH(X) = {:2.3f}'.format( -np.sum( p * np.log2( p ) ) ) )

# get and print average codeword length
L = np.sum( [ len( codewords[i] ) * p[i] for i in range(len(p)) ] )

print('Average codeword length: \tL = {:2.3f}'.format( L ) )


    

    




Max. Entropie: 			H0 = 3.322
Entropy: 			H(X) = 2.769
Average codeword length: 	L = 3.170

In [6]:

    

###
# you may, for example, optimize the generated code by eliminating
# unnecessary bits
###

# your code ###


    

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