This document discusses error detection techniques including cyclic redundancy checks (CRCs) and discusses the differences between bit rate errors and frame rate errors. It can be summarized as: 1. CRCs are a commonly used error detection technique where a check value is calculated based on the data and transmitted with it to allow the receiver to check for errors. 2. Bit rate error refers to the rate of errors in transmitted bits, while frame rate error refers to the ratio of data received with errors to the total data received. 3. A method is presented for estimating both bit error rate and frame error rate for low-density parity-check codes based on enumerating the smallest weight error patterns that cannot be corrected.

1. Error Detection
• CRC Calculation
• Frame rate error v/s Bit rate error
Presented by : Divya Dihuliya
Ishan Sharma
Riva
Modith

2. Content:
• Introduction
• Types of Errors
• Error Detection
• Cyclic Redundancy Check (CRC)
• Bit Rate Error
• Frame Rate Error
• Bit Rate Error v/s Frame Rate Error

3. Introduction
What is Error?
The end to end transfer of data from a Transmitter to a Receiver
involves many step, each subject to error.

4. Types of Errors
Single Bit Error : Only one
bit of data unit is changed
from either 0 to 1 or 1 to 0.
Burst Error : Two or more
bits in the data is changed.
Packet error are errors like
Packet loose/ Duplication/
Re-ordering.

5. Error Detection
Process of detecting errors between sender and
receiver.
Error Detection
Parity
Check
Check
sum
CRC

6. Cyclic Redundancy Check
CRCs are so called because the check (data verification) value is
a redundancy (it expands the message without adding
information) and the algorithm is based on cyclic codes.
Cyclic redundancy check (CRC) is an error-detecting code
commonly used in digital networks and storage devices to detect
accidental changes to raw data.
CRCs are popular because they are simple to implement in
binary hardware, easy to analyse mathematically, and particularly
good at detecting common errors caused by noise in
transmission channels.

7. CRC Calculation
View data bits (D) as a binary number.
Example : D = 101101101
Represent n bit message as (n-1) degree polynomial.
D(x) = x8 + x6 + x5 + x3 + x2 + 1
XOR operation
Data before sending.
Data after sending.
Receiver Test (To check if the data transmitted is non-corrupt).

8. A transmitter wishes to send a message D with d data
bits in it.
A CRC code R, with r bit of length must be added
before the data is sent.
D : d data bits R : r CRC bits
Receiver and Transmitter know a bit pattern
dominated (G), of generator.

9. Types of CRC’s:
Standard for CRC with 8,12,16 and 32 bits.
CRC-32 used by IEEE link protocols i.e. Ethernet.
CRC-8 used in ATM’s data communication.

10. BIT RATE ERROR
A bit error rate is defined as the rate at which errors
occur in a transmission system. This can be directly
translated into the number of errors that occur in a
string of a stated number of bits.

11. Bit error rate, in assessing systems.
Systems for which bit error rate, BER is applicable
include radio data links as well as fibre optic data
systems, Ethernet.
Bit error rate, BER, provides an ideal way in which the
necessary to assess the performance of the system can
be achieved.
Unlike many other forms of assessment, bit error rate,
BER assesses the full end to end performance of a
system including the transmitter, receiver and the
medium between the two.

12. If the medium between the transmitter and receiver is good and
the signal to noise ratio is high, then the bit error rate will be very
small.
The main reasons for the degradation of a data channel and the
corresponding bit error rate, BER is noise and changes to the
propagation path (where radio signal paths are used). Both
effects have a random element to them.
For fibre optic systems, bit errors mainly result from
imperfections in the components used to make the link. These
include the optical driver, receiver, connectors and the fibre
itself.
Another contributory factor for bit errors is any phase jitter that
may be present in the system as this can alter the sampling of
the data.

13. BER and Eb/No
Eb/N0 (the energy per bit to noise power
spectral density ratio) is an important
parameter in digital communication or data
transmission. It is a normalised signal to
noise ratio (SNR) measure, also known as
the "SNR per bit". It is especially useful
when comparing the bit error rate (BER)
performance.
It should be noted that each different type
of modulation has its own value for the
error function.
The energy per bit, Eb, can be determined
by dividing the carrier power by the bit rate
and is a measure of energy with the
dimensions of Joules.
No is a power per Hertz and therefore this
has the dimensions of power (joules per
second) divided by seconds.

14. Factors affecting the bit error rate
It can be seen from using Eb/No, that the bit error rate, BER can be affected by a
number of factors. By manipulating the variables that can be controlled it is
possible to optimise a system to provide the performance levels that are required.
Interference: By reducing the bandwidth the level of interference can be
reduced. However reducing the bandwidth limits the data throughput that can be
achieved.
Increase transmitter power: It is also possible to increase the power level of the
system so that the power per bit is increased. This has to be balanced against
factors including the interference levels .
Lower order modulation: Lower order modulation schemes can be used, but
this is at the expense of data throughput.
Reduce bandwidth: Another approach that can be adopted to reduce the bit
error rate is to reduce the bandwidth. Lower levels of noise will be received and
therefore the signal to noise ratio will improve. Again this results in a reduction of
the data throughput attainable.

15. Bit error rate testing
A data stream is sent through the communications channel,
whether a radio link, a fibre optic link or whatever, and the resulting
data stream is compared with the original. Any changes are noted
as data errors and logged. Using this information a bit error rate
can be determined.
The basic concept of a bit error rate test is straightforward, but the
actual implementation requires a little more thought, and is not as
simple. There are a number of issues that need to be addressed.
As data errors occur in a random fashion it can take some while
before an accurate reading can be gained using normal data. In
order to shorten the time required for measurements, a
pseudorandom data sequence can be used.

16. System simulation for BER
testing
In addition using a pseudo-random data source, it is often necessary to
simulate the transmission path. To simulate the transmission path it is
necessary to set up a "medium" that is representative of the actual data
transmission path to be used. In terms of a radio transmission, this includes
noise and propagation fading.
Noise: The receiver noise will be present regardless of whether the system
is in a simulated or real environment. The remaining noise can be simulated
and introduced to the receiver using a noise diode generator.
Fading characteristics for radio communications systems: It is very
important to simulate the real life characteristics of the transmission path in
as realistic a way as possible. To achieve this for a radio link it is necessary
to use a fading simulator that adds Rayleigh fading characteristics to the
signal.

17. Frame Rate Error
Ratio of data received with errors to the total data received. Used to determine the
quality of a signal connection. If the FER is too high (too many errors), the connection
may be dropped.
DATA FRAME :
A data frame is an aggregate of numerous, partly overlapping collections of data
and metadata that have been derived from massive amounts of network activity
such as content production, consumption, and other user behaviour. A data frame
may be used to drive the creation of new content, applications, or infrastructure
enhancements.

18. When data is corrupted

19. Framing error
Generally, a framing error is the result of starting to read a sequence
of data at the wrong point.
In serial communications, a framing error is the result of reading a
string of symbols which are grouped in blocks at the wrong starting
point. The symbols are bits and the blocks are bytes, ten bits in
asynchronous transmission and eight in synchronous. A framing error in
an asynchronous stream usually recovers quickly, but a framing error in
a synchronous stream produces gibberish at the end of the packet.
Framing errors can be detected with parity bits.

20. Estimation of BER and FER
A method for estimating the performance of low-density parity-check
(LDPC) codes decoded by hard-decision iterative
decoding algorithms on binary symmetric channels (BSC) is
proposed.
Based on the enumeration of the smallest weight error patterns
that cannot be all corrected by the decoder, this method
estimates both the frame error rate (FER) and the bit error rate
(BER) of a given LDPC code with very good precision for all
crossover probabilities of practical interest.

21. FER estimation

22. BER estimation

23. Thank you!!