The presentation discusses cyclic redundancy check (CRC) as an error-detecting code utilized in digital networks and storage systems. It highlights error detection and correction processes, the structure of encoders and decoders, and the use of polynomials in CRC operations. Additionally, it outlines the advantages of cyclic codes in error performance and their efficiency in implementation.

1. PRESENTATION ON
CYCLIC REDUNDANCY
CHECK(CRC)
PRESENTED BYSUDHANSHU SRIVASTAVA(210001)
ABHISHEK SINGH(210002)
SAURABH PRATAP SINGH(210003)
ASHUTOSH KUMAR CHATURVEDI(210005)

2. CONTENT
1. ERROR DETECTION
2.ERROR CORRECTION
3.CYCLIC REDUNDANCY CHECK(CRC)
4.CRC POLYNOMIAL
5.ADVANTAGE OF CYCLIC CODES

3. ERROR DETECTION
Error detection is the detection of errors caused by noise or other impairments
during transmission from the transmitter to the receiver. Summer is another
name for error detection.
The receiver can detect a change in the original code word.
• 1. The receiver has (or can find) a list of valid code words.
• 2. The original code word has changed to an invalid one.

4. PROCESS OF ERROR DETECTION

5. ERROR CORRECTION
• Error correction is the detection of errors and reconstruction of the original,
error-free data.
• error correction is much more difficult than error detection. In error detection,
the receiver needs to know only that the received code word is invalid.
• In error correction the receiver needs to find (or guess) the original code word
sent.
• we need more redundant bits for error correction than for error detection.

6. STRUCTURE OF ENCODER & DECODER IN
ERROR CORRECTION

7. CYCLIC REDUNDANCY CHECK (CRC)
• Cyclic codes are special linear block codes with one extra property. In a cyclic
code, if a code word is cyclically shifted (rotated), the result is another code
word.
• A cyclic redundancy check (CRC) is an error-detecting code commonly used
in digital networks and storage devices to detect accidental changes to raw
data.
• Blocks of data entering these systems get a short check value attached, based
on the remainder of a polynomial division of their contents; on retrieval the
calculation is repeated, and corrective action can be taken against presumed
data corruption if the check values do not match.

8. A CRC code with C(7,4)

9. CRC encoder and decoder

10. DIVISION IN CRC ENCODER

11. DIVISION IN CRC DECODER

12. USING POLYNOMIAL
• We can use a polynomial to represent a binary word.
• Each bit from right to left is mapped onto a power term.
• The rightmost bit represents the “0” power term. The bit next to it
the “1” power term, etc.
• If the bit is of value zero, the power term is deleted from the
expression.

13. CRC DIVISION USING
POLYNOMIALS

14. ADVANTAGES OF CYCLIC CODES
• Cyclic codes have a very good performance in detecting single-bit errors, double
errors, an odd number of errors.
• They can easily be implemented in hardware and software.
• They are especially fast when implemented in hardware.
• This has made cyclic codes a good candidate for many networks.