Error Calculations

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Error Calculations
Meaningful Error rates are mostly calculated in
terms of Signal-to-Noise Ratio
where dpulse density, Esenergy per symbol,
Ebenergy per bit, Lnumber of levels,
1/Tsignaling rate, NBW noise bandwidth
and N0power measured in a BW of 1 Hz.
Optimum signaling format is provided by minimum
error at a minimum noise bandwidth. A balanced
2-level coding can provide optimum performance.
Performance Monitoring
Performance monitoring determines BER by any of
these Redundancy Check can be performed by
Line Code redundancy or Logic level redundancy.
Bipolar violation is an example of Line Code
redundancy. Logic level redundancy is carried out
by insertion of parity bits or CRC bits. Signal
Quality Measurements Certain properties like
signal power are measured, error is estimated and
extrapolated for a very low error rate.
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Performance Parameters
Error Free Second (EFS) The percentage of time
available for Data transmission. Burst Errored
Second (BES) An error second with at least 100
errors. Errored Second (ES) A second with at
least one error. Severely Errored Second (SES) A
second with BER gt 10-3. Degrade Minute (DM) A
minute with BER gt 10-6. For a 27,000 km
reference connection, the accepted values are
ESlt8, SESlt0.2 and DMlt10. These 3 parameters
are ITU G.821.
Parity Error and BER
The relation between the Parity Error Rate (PER)
and Bit Error Rate (BER) is as follows
where Nnumber of bits used for parity and
pBER
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CRCER and BER
The relation between the Cycle Redundancy Check
(CRC) and Bit Error Rate (BER) is as follows
where Nnumber of CRC bits and pBER
Forward Error Correction
This is a method of adding redundant bits to
detect and correct errors. Available methods are
block encoding and convolution encoding.
Reed-Solomon coding is a popular form of
block Encoding.
TDM and Framing
Multiplexing is a technique of combining traffic
from different channels onto a single channel.
TDM is the most common form of multiplexing in
digital transmission. To allocate time slots
to individual channels frames containing bits or
words are interleaved to form the bit or data
stream.