smart-e 4K-RX9000, User Manual

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4K-9000 USER MANUAL V1.1
© 2018 Smart-e (UK) Ltd www.smart-e.co.uk PAGE | 11
6 BIT ERROR RATES
6.1 DEFINITION AND CALCULATION
A bit in digital communications can have two possible binary values, a ‘1’ or a ‘0’. A bit error is defined as when
a bit is received of an incorrect value due to timing synchronisation errors, interference or data distortion.
Example
Bit Number : 9 8 7 6 5 4 3 2 1
Data to be transmitted: 0 1 1 1 0 0 1 0 1
Data received : 0 0 1 1 0 1 0 0 1
In the above example 3-bits received are in error, bits 3, 4 and 8. A Bit Error Rate, abbreviated to BER, is
defined as the number of bits received in error per unit of time.
𝐵𝐸𝑅 =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑
If we assume that the nine bits from the example above are sent in 1 second, then the BER becomes
𝐵𝐸𝑅 =
3
9
= 0.333
This is an extreme example to illustrate the theory of errors, a digital medium in which these many errors were
seen would result in no output, especially for high bandwidth transmissions such as HD video.
It is more normal for a digital transmission to consist of many millions or even hundreds of millions of bits per
second. If we change the example so we still receive 3 errors but within this second 300 million bits are
transmitted the equation becomes
𝐵𝐸𝑅 =
3
300,000,000
= 0.00000001
This is a more realistic representation of the kinds of bit error rates seen in digital transmission systems,
however this is not the value usually presented. For simplicity the figure is presented in standard form
0.00000001 = 1𝑥10
−8
= 10
−8
= 10^ − 8
This is the form BER is presented and the form in which it is seen on the LCD display of the 4K-9000. If the
value does not contain a single 1 then the value is rounded up or down to the nearest single 1 value. For
example, 6.2x10^-7 becomes 1x10^-6 = 10^-6, 3.8x10^-7 becomes 1x10^-7 = 10^-7. A higher value is
therefore desired, the 4K-9000 can read from 10^-0 to 10^-10. 10^-
10 is a ‘perfect’ system with very little
error a 10^-0 reading means no video as there are too many errors.