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Usually, the received signal can no longer be modeled as a determinis noise (WGN). Instead, it ic signal in white Gaussian should be considered as a function of either the state of a Markov chain or of its state transition probabili observed in the WGN. Mar stochastic process where t depends only on the prese y with known parameters kov chain is a special kind of he outcome of an experiment nt state not on the preceding states. Markov chain is defined as the process with Figure 1: Channel adaptive error control scheme As shown in the figure 1, channel condition is estimated and the derived BER is divided into three ranges: lower, middle and higher. Depending on the BER range, error control scheme uses three modes to handle the erors. All the three modes are detailed in the figure. We have assumed low range of BER is from 10-9 to 10-12, mid range from 10-6 to 10-8 and high range from 10-3 to 10—5. For the low range, simple error control scheme without retransmission is used. For the middle range, error control scheme with retransmission is employed and for the high range, the error control is left to the upper layer. As BER depends on the SNR, its requirement is different for different services and systems. For instance, wireless link BER is less than 10—6 while optical BER is less than 10—12. On optical fiber link, the average BER is approximately 10—9 where as on a coaxial cable, the probability of bit errors is around 10—6. For a switched telephone line, these numbers are even higher between 10—4 and 10—5. Digitized voice can tolerate bit errors as high as 1 bit per thousand bits sent i.e 10-3. Computer data requires a BER of 10—6 to 10-12 (i.e. 1 per million to 1 per trillion) depending on the content.

Figure 1 Usually, the received signal can no longer be modeled as a determinis noise (WGN). Instead, it ic signal in white Gaussian should be considered as a function of either the state of a Markov chain or of its state transition probabili observed in the WGN. Mar stochastic process where t depends only on the prese y with known parameters kov chain is a special kind of he outcome of an experiment nt state not on the preceding states. Markov chain is defined as the process with Figure 1: Channel adaptive error control scheme As shown in the figure 1, channel condition is estimated and the derived BER is divided into three ranges: lower, middle and higher. Depending on the BER range, error control scheme uses three modes to handle the erors. All the three modes are detailed in the figure. We have assumed low range of BER is from 10-9 to 10-12, mid range from 10-6 to 10-8 and high range from 10-3 to 10—5. For the low range, simple error control scheme without retransmission is used. For the middle range, error control scheme with retransmission is employed and for the high range, the error control is left to the upper layer. As BER depends on the SNR, its requirement is different for different services and systems. For instance, wireless link BER is less than 10—6 while optical BER is less than 10—12. On optical fiber link, the average BER is approximately 10—9 where as on a coaxial cable, the probability of bit errors is around 10—6. For a switched telephone line, these numbers are even higher between 10—4 and 10—5. Digitized voice can tolerate bit errors as high as 1 bit per thousand bits sent i.e 10-3. Computer data requires a BER of 10—6 to 10-12 (i.e. 1 per million to 1 per trillion) depending on the content.

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Figure 3: Markov chain representation of errors where s is the number of states in the Markov chain and p is the transition probability from current to next state where as (1— p) is the probability to remain in the same state. Using these transition probabilities, one can establish an asymptotic formula for the capacity of a BSC as the noise parameter tends to zero. To capture the bursty nature of wireless networks, Markov chains have been extensively used to model the error sequences generated by a wireless channel where a BSC is associated with each state. TheMarkov chain provides a good approximation of the error process in fading channels. Here, the Markov state and transition probabilities between the states are assumed. As shown in the figure 3, the probability pj (n) = P(Xn = }) is the probability of the system to reach state j inn steps. For instance, p2(1) = P(X1 = 2) is the probability to reach state 2 from state 1 in one step. The channel states associated with consecutive symbols are assumed to be the neighboring states for a slow fading channel where the SNR varies slowly as the symbol interval T increases. Each state describes the SNR level received as the interval T increases. In order to estimate the errors, we need to find out the expression for BER in terms of SNR using the standard deviation and mean. To estimate the BER, the system should move from one state to another in both the directions from good to bad and vice versa. The type of random noise in a communication system that determines the BER of a circuit is the thermal noise which can well be described by additive white Gaussian (AWG) noise across a narrow frequency band. Even though it is possible to have other types of noise from the interfering signals that combine with thermal noise in the final BER, the type of noise addressed here is purely Gaussian. where Cb is Boltzmann’s constant and Ttotal is system noise temperature in Kelvin. Note that Ttota the sum of all the individual noise temperatures in he previous gains in the system system normalized by t The Gaussian distributi to detect an observed standard deviation of probability of a signal being misinterpreted (or in error) by the system, one just needs to know the number standard deviations tha average signal level so that the signal can cross threshold value. The equation 3 on provides with the probabi value given the mean and he measurement. To know is added or subtracted from he is he ity he he of he he n this number of standard deviations is related to the probability, (P) of an error occurring, using the Gaussian function as shown in
Figure 3: Markov chain representation of errors where s is the number of states in the Markov chain and p is the transition probability from current to next state where as (1— p) is the probability to remain in the same state. Using these transition probabilities, one can establish an asymptotic formula for the capacity of a BSC as the noise parameter tends to zero. To capture the bursty nature of wireless networks, Markov chains have been extensively used to model the error sequences generated by a wireless channel where a BSC is associated with each state. TheMarkov chain provides a good approximation of the error process in fading channels. Here, the Markov state and transition probabilities between the states are assumed. As shown in the figure 3, the probability pj (n) = P(Xn = }) is the probability of the system to reach state j inn steps. For instance, p2(1) = P(X1 = 2) is the probability to reach state 2 from state 1 in one step. The channel states associated with consecutive symbols are assumed to be the neighboring states for a slow fading channel where the SNR varies slowly as the symbol interval T increases. Each state describes the SNR level received as the interval T increases. In order to estimate the errors, we need to find out the expression for BER in terms of SNR using the standard deviation and mean. To estimate the BER, the system should move from one state to another in both the directions from good to bad and vice versa. The type of random noise in a communication system that determines the BER of a circuit is the thermal noise which can well be described by additive white Gaussian (AWG) noise across a narrow frequency band. Even though it is possible to have other types of noise from the interfering signals that combine with thermal noise in the final BER, the type of noise addressed here is purely Gaussian. where Cb is Boltzmann’s constant and Ttotal is system noise temperature in Kelvin. Note that Ttota the sum of all the individual noise temperatures in he previous gains in the system system normalized by t The Gaussian distributi to detect an observed standard deviation of probability of a signal being misinterpreted (or in error) by the system, one just needs to know the number standard deviations tha average signal level so that the signal can cross threshold value. The equation 3 on provides with the probabi value given the mean and he measurement. To know is added or subtracted from he is he ity he he of he he n this number of standard deviations is related to the probability, (P) of an error occurring, using the Gaussian function as shown in
net eg ee ee Ee As shown in the figure 6, the throughput fluctuates for various SNR values for a fixed number of frame lengths. However the throughput increases as the SNR increases. This is because, as the SNR increases, the number of errors in the frame decreases thereby Figure 6: Throughput Vs.SNR increasing the number of frames delivered thus increasing the throughput. The throughput is. slightly more for DCAECS compared to ASAEC since in the case of ASAEC, the throughput increases with SNR slowly. In case of DCAECS, the throughput increases fast with various SNR values.
net eg ee ee Ee As shown in the figure 6, the throughput fluctuates for various SNR values for a fixed number of frame lengths. However the throughput increases as the SNR increases. This is because, as the SNR increases, the number of errors in the frame decreases thereby Figure 6: Throughput Vs.SNR increasing the number of frames delivered thus increasing the throughput. The throughput is. slightly more for DCAECS compared to ASAEC since in the case of ASAEC, the throughput increases with SNR slowly. In case of DCAECS, the throughput increases fast with various SNR values.
Figure 7: Probability of Errors Vs. Number of Errors for different message lengths plotted against frame lengths for different values of BER. As the frame length increases, the PRTx also increases slowly and remains constant at some point (L = 200bits). This plot indicates that PRTx initially increases and later remains stable as the frame length increases.
Figure 7: Probability of Errors Vs. Number of Errors for different message lengths plotted against frame lengths for different values of BER. As the frame length increases, the PRTx also increases slowly and remains constant at some point (L = 200bits). This plot indicates that PRTx initially increases and later remains stable as the frame length increases.
as a Pees Wee TEESE RAST SA) era’ She Although ASAEC “speaks about ARQ, it does not analyze the probability of retransmissions where as DCAECS discusses about probability retransmission for different frame lengths. As shown in the graph in figure figure 8, the probability of retransmission is PRTXx is
as a Pees Wee TEESE RAST SA) era’ She Although ASAEC “speaks about ARQ, it does not analyze the probability of retransmissions where as DCAECS discusses about probability retransmission for different frame lengths. As shown in the graph in figure figure 8, the probability of retransmission is PRTXx is
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