Post on 23-Jul-2020
Transmission of Audio Files using Random Codes Basedon Quasigroups
Vladimir Ilievski1 Aleksandra Popovska-Mitrovikj1 Verica Bakeva1
1Faculty of Computer Science and Engineering
LOOPS, 2015
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 1 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 2 / 31
Introduction
Transmission of audio files through a binary-simetric channel
Coding/Decoding algorithms: Cut-Decoding and 4-Sets-Cut-Decoding
Code (72, 576) with rate R = 18
Experiments with Beethoven‘s ”Ode to Joy”
Analyzing the results
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 3 / 31
Random Codes Based On Quasigroups
Combination of coding/decoding and encryption/decryptionalgorithms
The algorithms are using the alphabet of nibblesQ =
{0, 1, ..., 9, a, b, c , d , e, f
}The message that needs to be transmitted is structured in a packetsof 18 nibbles
Packet-error rate:
PER =#(incorrectly decoded packets)
#(all packets)
Bit-error rate:
BER =#(incorrectly decoded bits in all packets)
#(bits in all packets)
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 4 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 5 / 31
Cut-Decoding Algorithm
Modification of the standard RCBQ algorithm for better performances
4.5 times faster than the standard one
Detailed description of the algorithm is given in ??
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 6 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 7 / 31
4-Sets-Cut-Decoding Algorithm
Modification of the Cut-Decoding algorithm
Increasing the coding and decoding speed
Detailed description of the algorithm is given in []
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 8 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 9 / 31
Representing Audio Files
Sequence of samples and sampling rate
Samples are values in range [−a, a] where a can be power of 2
Sample rate is the number of samples of audio carried per second,measured in Hz
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 10 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 11 / 31
Converting Audio File to Nibbles
Using Matlab function audioread[y ,Fs ]
y is the sequence of sample values, Fs is the sample rate
Converting sample values to 32-bit integer numbers
Adding 32768 on every sample value
Converting every sample value to a four digit hexadecimal number
Creating messages as a sequence of 18 hexadecimal digits
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 12 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 13 / 31
Converting Nibbles to Audio File
Using Matlab function audiowrite[y ,Fs ]
y is the sequence of sample values, Fs is the sample rate
Dividing the output in a 4 digit hexadecimal numbers
Converting 4 digit hexadecimal numbers to integers and subtracting32768
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 14 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 15 / 31
Original AudioBeethoven‘s Ode to Joy
Beethoven‘s Ode to Joy
Total number of packets:43008
Total number of bits: 43008 ∗ 18 ∗ 4 = 3096576
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 16 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 17 / 31
Cut-Decoding AlgorithmProbability of Error p = 0.05
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.05
Figure: Difference for p = 0.05
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 18 / 31
Cut-Decoding AlgorithmProbability of Error p = 0.08
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.08
Figure: Difference for p = 0.08Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 19 / 31
Cut-Decoding AlgorithmProbability of Error p = 0.11
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.11
Figure: Difference for p = 0.11
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 20 / 31
Cut-Decoding AlgorithmPER and BER
Table of experimental results for PER and BER
p PER BER
0.05 0.001697359 0.000913267
0.08 0.023111979 0.011926399
0.11 0.113071987 0.057805137
Table: Experimental Results using Cut-Decoding
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 21 / 31
Outline
1 Introduction
2 Random Codes Based On QuasigroupsCut-Decoding Algorithm4-Sets-Cut-Decoding Algorithm
3 Audio FilesRepresenting Audio FilesConverting Audio File to NibblesConverting Nibbles to Audio File
4 Experimental ResultsOriginal Audio Beethoven‘s ”Ode to Joy”Experimental Results Using Cut-Decoding AlgorithmExperimental Results Using 4-Sets-Cut-Decoding Algorithm
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 22 / 31
4-Sets-Cut-Decoding AlgorithmProbability of Error p = 0.05
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.05
Figure: Difference for p = 0.05
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 23 / 31
4-Sets-Cut-Decoding AlgorithmProbability of Error p = 0.08
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.08
Figure: Difference for p = 0.08
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 24 / 31
4-Sets-Cut-Decoding AlgorithmProbability of Error p = 0.11
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.11
Figure: Difference for p = 0.11
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 25 / 31
4-Sets-Cut-Decoding AlgorithmProbability of Error p = 0.14
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.14
Figure: Difference for p = 0.14
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 26 / 31
4-Sets-Cut-Decoding AlgorithmProbability of Error p = 0.17
Difference between the original(orange colored) and transmitted(bluecolored) audio file for p = 0.17
Figure: Difference for p = 0.17
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 27 / 31
4-Sets-Cut-Decoding AlgorithmPER and BER
Table of experimental results for PER and BER
p PER BER
0.05 0.000581287 0.00026061
0.08 0.007091704 0.003033027
0.11 0.034249442 0.015375047
0.14 0.129580543 0.056156219
0.17 0.34749349 0.153494376
Table: Experimental Results using 4-Sets-Cut-Decoding
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 28 / 31
4-Sets-Cut-Decoding AlgorithmPER and BER
Plot of experimental results for PER
0 4 · 10−2 8 · 10−2 0.1 0.12 0.14 0.16 0.18
5 · 10−2
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Probability of error p
PER
PER dependence of p
PER
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 29 / 31
4-Sets-Cut-Decoding AlgorithmPER and BER
Plot of experimental results for BER
0 4 · 10−2 8 · 10−2 0.1 0.12 0.14 0.16 0.18
5 · 10−2
0.1
0.15
0.2
Probability of error p
BER
BER dependence of p
BER
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 30 / 31
For Further Reading I
A. Author.Handbook of Everything.Some Press, 1990.
S. Someone.On this and that.Journal of This and That, 2(1):50–100, 2000.
Vladimir Ilievski, Aleksandra Popovska-Mitrovikj, Verica Bakeva (”Ss Cyril and Methodius” University in Skopje)Transmission of Audio Files using Random Codes Based on QuasigroupsLOOPS, 2015 31 / 31