BIT Error Rate

1. Bit Error Rate Pawan Kumar Tiwari MCA 5 th sem Roll No-15

2. Introduction Bit Error Rate (BER) is an important concept to understand in any digital transmission system since it is a major indicator of the health of the system. As data is transmitted some of the bits may not be received correctly. The more bits that are incorrect, the more the signal will be affected. Its important to know what portion of the bits are in error so you can determine how much margin the system has before failure.

3. What is BER? T he performance of digital receiver is measured by a parameter called the Bit-Error Ratio (BER ) BER is defined as the ratio of the number of wrong bits over the number of total bits. Sent Bits 1101101101 Received Bits 110 101101 error BER = No of bits in error/total bits transmitted Or wrong bits per sec/Data rate in bits per sec 10 0.1 1 = “ For a satisfactory performance the BER has to be less than ” .

4. Example Average rate of bit error For instance of 10000 bits are transmitted, 100 bits are received in error then average BER is = 100/10000 = 1% or 0.01 “ Bit error rate is frequently expressed as Probability P e ” [ 0<= P e <=0.5 ] Here 0.5 is maximum BER

5. Bit Error Probability The  bit error probability   p e   is the expectation value of the bit error ratio. The bit error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors . Example As an example, assume this transmitted bit sequence: 1 1 0 0 0 1 0 1 1 and the following received bit sequence:    1 0  1  0 1 0   1, The number of bit errors (the underlined bits) is, in this case, 3. The BER is 3 incorrect bits divided by 10 transferred bits , Resulting in a BER of 0.3 or 30%.

6. Packet Error R atio The  packet error ratio  (PER) is the number of incorrectly received data packets divided by the total number of received packets. A packet is declared incorrect if at least one bit is erroneous. The expectation value of the PER is denoted  packet error probability   p p , which for a data packet length of  N  bits can be expressed as p p = 1 - ( 1 – p e ) N Assuming that the bit errors are independent of each other. For small bit error probabilities, this is approximately

7. Noise and Intermittents Errors caused by noise or intermittent causes can have the same BER, but very different effects. Errors that are spread out are due to noise problems Errors that are grouped are due to intermittent problems such as ingress or loose connectors. Spaced Errors 11 11010110 1 00 1 110 Burst Errors 1111101011 1011 01101 This Example Shows the Same Error Rate But the Burst Errors are More Difficult to Correct

8. Error Seconds To get an idea of whether the errors are caused by noise or intermittent problems, errors can be measured over a one second period. If no errors are seen in a one second period, this is known as a Error Free Second . If some errors are received in a one second period that can't be handle by the FEC and seen by the end-user, this is known as a Error Second . If errors in a one second period that the FEC can't handle exceed  a set threshold, this is known as a Severely Errored Second . A Severely Errored Second has a BER within that second of 1E-6 or worse at the output of the FEC.

9. Bit E rror Rate t est A BERT (bit error rate test or tester) is a procedure or device that measures the BER for a given transmission. A bit error rate tester (BERT), also known as a  bit error ratio tester. The main building blocks of a BERT are: Pattern generator, which transmits a defined test pattern to the test system Error detector connected to the test system, to count the errors generated by or test system Clock signal generator to synchronize the pattern generator and the error detector Digital communication analyzer is optional to display the transmitted or received signal. Electrical-optical converter and optical-electrical converter for testing optical communication signals.

10. Bit Error R ate Of a Wireless System BER = or = 1/(2*SNR)     ( 1- )

11. Example-1 Compute a bit error rate of a wireless communication system at SNR=20 db 20 db = 10 log 10 SNR log 10 SNR = 2 SNR = 10 2 BER = 1/(2*SNR) = 1/(2 *100) = 0.5 * 10 -3 = 5 * 10 -4

12. Example-2 Compute SNR db of wierless communication system for BER=10 -6 ? 10 -6 = 1/(2*SNR) SNR = 1/2*10 -6 SNR = 10 6 /2 SNR db = 10 log 10 (10 6 /2) SNR db = 10*(log 10 (10 6 )) - 10 *(log 10 2) SNR db =60 db – 3db SNR db =57db

13. The Figure shows the signal current when bit-0 is transmitted and when bit-1 is transmitted. The figure also shows the probability density function of the current in the two binary states . For BER calculation it is assumed that the noise is almost Gaussian with standard deviations and , and means respectively for the 0 and 1 binary levels. For an optical receiver, in general the two standard deviations are different. For thermal noise dominated regime the two become same.  

14. The decision threshold is . That is So a bit error occurs when bit-0 is transmitted and When bit-1 is transmitted and The BER for an unbiased data ( a data which has statistically equal number of 0 and 1 bits), the BER is given as Where is the probability of error in bit-1, i.e. probability of current remaining below the threshold when actually bit-1 has been received. is the probability of error in bit-0, i.e. probability of current becoming greater than or equal to the threshold when actually bit-0 has been received.

15. References nptel .ac.in/courses/ Webcourse -contents/IIT%20Bombay/.../ FOC-Noise- BER .doc http://nptel.ac.in/courses/117104099 / http:// www.ijser.org/researchpaper%5COptimization-Method-for-Analysis-of-Bit-Error-Rate-with-BPSK-Modulation-Technique.pdf http:// www.ijarcsse.com/docs/papers/Volume_4/6_June2014/V4I6-0265.pdf https://en.wikipedia.org/wiki/Bit_error_rate

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