Effect of Error Packetization on the Quality of Streaming Video in Wireless Broadband Networks

A Markov model describing the duration of error intervals and error-free reception for streaming video transmission was developed based on the experimental data obtained as a result of streaming video from a mobile source on IEEE 802.16 standard network. The analysis of experimental results shows that the average quality of video sequences when simulating Markov model of packetization of errors are similar to those obtained when simulating single packet errors with PER index in the range of . An algorithm for creating software for simulating packetization of errors was developed. In this paper we describe the algorithm, software developed based on this algorithm as well as the Markov model created for the modeling. Keywords-Video streaming; Markov model; IEEE 802.16; Bit Error Rate; Burst Error Length; Packet Error Rate; Codec. I. INTRODUCTION The need to create realistic simulation and mathematical models of behavior of losses in the communication channels based on the apparatus of Markov chains for wireless access systems is a scientific problem of important consequence. Markov processes with the necessary number of states sufficiently describe the mechanism of transmission of information (1), the knowledge of which is necessary to analyze network problems during packet video transmission. The parameters of the model make it possible to determine the quality of transmitted video as well as the statistical parameters of the network. A model decscribing the length of error intervals and error- free reception for streaming video transmission was developed based on the experimental data obtained as a result of streaming video from a moving source on WiMAX network (2). Based on the graph of packet loss distribution, an array was formed in which the lost packet corresponds to a logic zero (0) and received packet corresponds to a logic unit (1). The original array was split into two, one of which contains information about the lost packets and the other contains information about the received packets. The formation of arrays was carried out in accordance with the procedure shown in Figure 1. II. MARKOV MODEL DESCRIBING THE EXPERIMENTAL DATA


INTRODUCTION
The need to create realistic simulation and mathematical models of behavior of losses in the communication channels based on the apparatus of Markov chains for wireless access systems is a scientific problem of important consequence.Markov processes with the necessary number of states sufficiently describe the mechanism of transmission of information [1], the knowledge of which is necessary to analyze network problems during packet video transmission.The parameters of the model make it possible to determine the quality of transmitted video as well as the statistical parameters of the network.
A model decscribing the length of error intervals and errorfree reception for streaming video transmission was developed based on the experimental data obtained as a result of streaming video from a moving source on WiMAX network [2].Based on the graph of packet loss distribution, an array was formed in which the lost packet corresponds to a logic zero (0) and received packet corresponds to a logic unit (1).The original array was split into two, one of which contains information about the lost packets and the other contains information about the received packets.The formation of arrays was carried out in accordance with the procedure shown in Figure 1.

II. MARKOV MODEL DESCRIBING THE EXPERIMENTAL DATA
In accordance with the method presented in [3], the available raw data file was divided into two parts, each of which separately contains the duration of ON periods and OFF periods.Variables y [n] fall under the ON periods, while variables y n [n] fall under the OFF peroids.An approximation of the distribution function (DF) of real processes is obtained.Equation ( 1) is used for approximating the distribution function of OFF state.

( ) ∑ ( )
By using the method of least squares we find the unknown coefficients of the approximation for the expression (1) as presented in Table 1.The unknown coefficients of the approximation for the expression (3) are found using the method of least squares and presented in Table 2. Substituting the coefficient values obtained and given in Table 2 into equation ( 3), we obtain the approximation of the original distribution of the length of ON periods as equation ( 4): The approximation of DF of ON is shown in Figure 2.
After the normalization of obtained approximating expressions ( 2) and ( 4), additional distributions of duration of ON-and OFF-processes, the matrix of transition probabilities are created, which is of the form presented in Figure 3: Substituting the values of the coefficients found in Tables 1  and 2 into the matrix of transition probabilities, we obtain the matrix of values in Figure 4.

III. SOFTWARE FOR ERROR PACKETIZATION SIMULATION
Simulation of the transmission of streaming video traffic over a WiMAX network can be done given the probability transition matrix and vector of initial probabilities [4].The choice of the initial state of the system was carried out using the condition that all states are equiprobable (i.e.p 1 N ⁄ , where N-number of states the system can be in after DF approximation).Description of the block diagram of the simulation algorithm is as given below, while the Markov model is shown in Figure 5.

IV. DESCRIPTION OF ERROR PACKETIZATION ALGORITHM STEP 1. Start program (Description of the variables, functions,
procedures and modules used) STEP 2. Enter two-dimensional array matrix of transition probabilities.In the developed software, this matrix was given as an array of constants in the declarations section and named markov.STEP 3. Set state from which to begin modeling.Since a 9state model was chosen, the state variable can take integer values on the interval (1 -9).Also, at this stage of the algorithm the accumulated variables summa_on and summa_off, which reflect the duration of the ON periods and OFF periods, are reset to zero respectively.STEP 4. Begin cycle with parameter i.The number of iterations equals the number of transitions in the simulated system.STEP 5. Instantiate the built-in generator of pseudorandom uniformly distributed sequence, generating a random value in the interval (0, 1).Assign the generated value to rnd.At the moment of generating the variable rnd, the system moves to the next state.The exact state into which it falls will be determined by the subsequent actions of the algorithm.The variable summa is reset to zero.STEP 6. Start the cycle with parameter k.The number of iterations in the cycle equals the number of states of the system being modeled.For this case, the number of iterations is eight (8).This loop is used to determine the state into which of the system has moved at the particular time of consideration.STEP 7. Checkdoes the value of rnd fall in the k th state of the Markov chain.At the same time the following variables are involved: summa -accumulates the probability of all states up to the k th ; markov [state, k]a two-dimensional array, which contains the transition matrix.If rnd falls within a range of probabilities corresponding to the k th state, then goto step 8, otherwise goto step 9. STEP 8. Checkin which state is the process currently?If in the active state, then goto step 10.If in passive state, then goto step 11.STEP 9.The summa variable is increased by the value of the probability of being in state k.Then proceed to the next iteration of step 6.STEP 10.Checkwas the last state of the matrix passive?If yes, goto step 12. Otherwise, goto step 16.STEP 11.Checkwas the last state of the matrix active?If yes, goto step 13.Otherwise, goto step 17 STEP 12. Arrival at this step implies the end of OFF period.
Therefore save or print to file summa_off.STEP 13.Arrival at this step implies the end of ON period.
Therefore save or print to file summa_on.STEP 14.Since the OFF period as ended, reset the variable summa_off to zero in preparation for the record of fresh OFF-period information, when the process will be in the passive state.STEP 15.Since the ON period as ended, reset the variable summa_on to zero in preparation for the record of fresh ON-period information, when the process will be in the active state.
STEP 16.Arrival at this step implies either the continuation of the previous ON period, or the start of a new ON period.So increment the variable summa_on and assign the value of cycle k to the state variable.STEP 17. Arrival at this step implies either the continuation of the previous OFF period, or the start of a new OFF period.So increment the variable summa_off and assign the value of cycle k to the state variable.STEP 18.At this step of the algorithm, the system just transited to the next state, so turn to the next iteration of the parameter i. STEP 19.End program.
As a result, the amount of packets falling either in the received state or the lost state in a row is accumulated ( ).
V. DISCUSSION Distribution function of ON-and OFF-processes for both the simulated and experimental sequences was obtained using the described Markov model shown in Figure 6.
Experiments show that increasing the number of states of the Markov model describing the packetization of errors allows for obtaining a satisfactory correspondence between the results of the experimental data and the data obtained by simulation.

A. Markov Model of Packetization of Errors
Two independent datasets, each containing 300,000 values were generated with the aid of the developed Markov model [5].This amount of data allows for a qualitative comparison of RTP packets from the experiment conducted on the transmission of a 30-minute streaming video on a real WiMAX network [2] with the results of the experiment conducted using the HSC.
In the model, each value in the array is represented by the numbers 0 or 1, where 0 means error-free value, and 1erroneous value.Figure 7 shows the distribution of data set values, where the white areas correspond to error-free values (0), and black -erroneous values (1).

Figure 6 .
Figure 6.DF of simulated samples of the length of OFF-(a) and ON (b) -periods: curve 1 -experiment, curve 2 -simulation

Figure 7 .
Figure 7. Distribution of error-free and erroneous values for rr ys №1 nd №2.

Figure 11 .Figure 9 .
Figure 11.Histogram and distribution function of the PSNR indicator in experiments №1 nd №2