modeling the effect of packet loss on speech quality: genetic programming based symbolic regression

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Modeling the Effect of Packet Loss on Speech Quality:Genetic Programming Based Symbolic Regression

Adil Raja

[email protected]

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Contents

• Packet Loss Modeling approaches: Related Research

• Current Approach.

• A Brief Intoduction to Genetic Programming (GP).

• Simulation Environment and GP Parameters.

• Analysis and Results.

• Conclusion and Future Aspirations.

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Packet Loss Modeling Approaches

Packet Based Approaches.• Based on regression of packet loss parameters to MOS.• Parameters include mean Loss rate, conditional loss probability etc.• Some approaches include:

. Markov Models [1].

. Regression Using Artificial Neural Networks. [2] [3] [4]

Speech Based Approaches• Intrusive: ITU-T Recommendation P.862 (PESQ).• Non-intrusive: ITU-T Recommendation P.563 (PSEAM).• Non-intrusive PESQ [5].

Adil Raja, Wireless Access research Centre University of Limerick, June 2006 3

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Our Previous Work

ANN based Regression of network traffic metrics on speech quality.• Useful Network loss Metrics.• Mean Loss Rate.• Means and Variances of Burst and Gap Length Distributions.• Codec Type and Packetization Interval.• Inter Loss Distance/Gap Length.

Packet loss was modeled using a Gilbert Model.

Results: -• rtraining=0.9835;• rvalidation=0.9821;• rtesting=0.9763


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Packet Loss Simulation

The Gilbert-Elliot Loss Model.

p =

n−1∑i=1

mi/m0

/mi

q = 1−

n−1∑i=2

mi × (n− 1)

/

n−1∑i=1

mi × i

π1 =p

p + q


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Packet Loss Simulation ...

Parameters of Geometrically Distributed Burst and Gap Lengths• Mean Burst Length = 1/q• Variance of Burst Length Distribution = (1-q)/q2

• Mean Gap Length = 1/p• Variance of Gap Length Distribution = (1-p)/p2

The Gilbert Model:• Packet loss can be simulated for certain values of p and q.• During network operation bursts have to be captured for determining clp and ulp.• The Gilbert model also models the packet loss due to jitter buffer discard/overflow.


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Current Approach and Experimental Details

• Genetic Programming has been used for mapping the effect of VoIP traffic parameters on speechquality.

• Codecs: G.729 and G.723.1 and AMR-NB.

• Packet/frame loss simulation is done using Gilbert Model.

• Mean Loss rate (ulp) was set to 10, 20, 30 and 40 %. clp was set to 10, 60, 80 and 90 %.

• Input Variables.. Mean loss rate.. Means and variances of burst and gap length distributions (VAD).. Codec type and packetization interval.. VAD: Different packets have different importance [6].

• From a total of 1408 speech files:. 35% were used for training.. 15% were used for validation.. 50% were used for Speaker independent testing.

• Speech activity - 70-80%


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A Brief Introduction to Genetic Programming (GP)

• GP is a Machine Learning Technique inspired by biological evolution. A branch of EvolutionaryAlgorithms.

• Aimed at evolving program expressions/computer code.

• Each individual encodes a symbolic expression.

• Solution Representation.. A tree structure is the most popular representation.. Other representations include graphs and linear structures such as arrays.

• Primary application area is modelling.. Commercial Application - predicting stock index.. Scientific Application - modelling physical processes.. Engineering Application - reverse engineering, designing circuitry, regression, classifica-

tion.. Data Mining.


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A simplified GP Breeding Cycle

GP uses four steps to solve problems:• Generate an initial population of random compositions of the functions and terminals of the

problem (computer programs).. Functions: plus, minus, times, sin, cos, mylog, mypower, divide, sqrt, mylog2, mylog10.. Terminals: Can be variables (network traffic parameters) and constants.

• Execute each program in the population and assign it a fitness value according to how well itsolves the problem.

. Minimization of χ2 error.

. Minimization of MSE (✓).

. Maximization of Pearson’s product moment correlation coefficient.

• Copy the best existing programs (Selection).. Roullete Wheel Selection - Fitness Proportinate Selection.. Tournament Selection.. Lexicographic Parsimony Pressure (✓).. ...

• Create new computer programs by mutation and crossover.


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A simplified GP Breeding Cycle: A Symbolic Representation


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Mutation

Two types of mutation are possible1:• A terminal replaces a terminal or a function replaces a function.• A subtree can replace an entire subtree.

1http://www.geneticprogramming.com/Tutorial/#anchor181526


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Crossover

Two solutions are recombined to form two new solutions or offspring.


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The GP Environment

GPLAB - A Matlab tool-box by Sara Silva ([email protected]).

Other GP Parameters• Survival: Replacement (✓), Elitism.• Adaptive genetic operator probabilities.• Initial Population Size: 100.• Generational Gap: 1.

Linear Scaling [7]MSE (y, t) = 1/n

n∑i

(ti − yi)2

MSEs (y, t) = MSE (a + by, t) = 1/nn∑i

(ti − (a + byi))2

a = t̄− b ¯f(x)

b =cov(t, y)

var(y)


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Advantages of Linear Scaling

• Bloat Control.

• Faster Training.

• Solutions better suited for real-time evaluations.


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Analysis and Results

A total of 50 runs were performed. Each run was spanned over 50 gener-ations.

Fitness Curves:


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Analysis and Results ...

Diversity and Tree Size plots


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Parameter Representation in GP Environment

GP Representation ParameterX1 codec typeX2 Packetization Interval (PI)X3 Mean Loss Rate (mlr)X4 Mean Burst Length (mbl)X5 Mean Gap Length (mgl)X6 Variance of Burst Length (vbl)X7 Variance of gap length (vgl)

• Talkspurt based values of all the parameters are used.


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• Fitness= 0.0523; Test Fitness=0.0496 rtraining=0.9074;rvalidation=0.9183;


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Analysis and Results

• A less bloated solution.

• Fitness= 0.0670; Test Fitness=0.0555 rtraining=0.8796rvalidation= 0.9079;

GP −MOS − LQO = −2.3843[sin

(√X3 + sin (X3)

)]+ 3.6112


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• Fitness= 0.0678; Validation Fitness=0.0556; Test Fitness=0.0650; rtraining=0.8780rvalidation=0.9074; rtesting=0.8881.

GP −MOS − LQO = −3.3432[√

X3]

+ 3.6881


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• Fitness= 0.0678; Validation Fitness=0.0556; Test Fitness=0.0650; rtraining=0.8780rvalidation=0.9074; rtesting=0.8881.

GP −MOS − LQO = −10.0296

[√X3/9

]+ 3.6881


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Conclusions and Future Aspirations

• Results obtained by GP have advantages over other machine learning algorithms (such asANNs).

. Simplified results: A mathematical expression.

. GP searches for global minimum of the error function and is less prone to getting stuckin local minima (due to mutation property).

. The prelimanary results are not comparable to ANN based approaches but there isroom for improvement.

• Improvements: Some Speculations; The Known Knowns.. Population size should be increased to 500 for the sake of having more diverse search

space.. Selection: Lexicographic parsimony pressure vs Tournament selection.. Survival: Replacement vs some elitism criterion.

• The work can be split to two parts:. The Telecommunications intensive aspects.. The GP intensive aspects.

• Developing an in-depth understanding of GP shall be a part of future endeavors.


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Thanks!


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References

[1] A. D. Clark. "Modeling the effects of burst packet loss and recency on subjective voice quality".In 2nd IP-Telephony Workshop, Columbia University, New York, April 2001.

[2] S. Mohamed, F. Cervantes-Perez, and H. Afifi. "Integrating networks measurements and speechquality subjective scores for control purposes". In Annual Joint Conference of the IEEE Computerand Communications Societies (INFOCOM), pages 641Ű649, 2001.

[3] S. Mohamed, G. Rubino, and M. Varela. "A method for quantitative evaluation of audio qualityover packet networks and its comparison with existing techniques". In Measurement of Speech andAudio Quality in Networks (MESAQIN), 2004.

[4] L. F. Sun and E. C. Ifeachor. "Perceived speech quality prediction for voice over ip-based networks".In IEEE International Conference on Communications (ICC), volume 4, pages 2573 -Ű 2577, 2002.

[5] A.E. Conway, "Output-based method of applying PESQ to measure the perceptual quality offramed speech signals", IEEE Communications Society, 2004.

[6] L. Sun, G.Wade, B. M. Lines, and E. C. Ifeachor. "Impact of packet loss location on perceivedspeech quality". In 2nd IP-Telephony Workshop, Columbia University, New York, April 2001.

[7] M. Kaijzer. "Scaled Symbolic Regression". 2003.


modeling the effect of packet loss on speech quality: genetic programming based symbolic regression

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