“Data can be corrupted during transmission. For reliable communication,

errors must be detected and corrected.”

ERROR CORRECTION

MODULE 8

- a character is received in error, rather than to revert to a higher level of error correction or display the incorrect character, a unique character that is undefined by the character code.

1. SYMBOL SUBSTITUTION

2. RETRANSMISSION

– is when a message is received in error and the receive terminal automatically calls for retransmission of the entire message.

- often called ARQ ( Automatic Request for Retransmission )

3. FORWARD ERROR CORRECTION

– is the only error correction scheme that actually detects and corrects transmission errors at the receive end without calling for retransmission.

HAMMING CODE

-developed by R.W. Hamming-the number of bits in the Hamming code is dependent on the number of bits in the data character -the number of bits that must be added to a character is determined from the following expression:

HAMMING CODE

where:n – number of Hamming bitsm – number of bits in the data character

EXAMPLE 1

1. For a 12-bit data string of 101100010010, determine the number of Hamming bits required, arbitrarily place the Hamming bits into the data string, determine the condition of each Hamming bits, assume an arbitrary single-bit transmission error, and prove that the Hamming code will detect the error.

EXAMPLE 22. The Hamming bits are to be

inserted into bit positions 1, 2, 4, 8 etc. Determine each of the following:

a. The number of Hamming bits required for the

data block given below. b. The (m+n, k) block check code

EXAMPLE 2

c. The Hamming code for the data block given below.

d. The code efficiencye. The code redundancy

EXAMPLE 3

3. The Hamming bits appear in bits positions 1, 2, 4, 8 and 16. The following (16, 11) block check code is received at a receiver. Determine whether the data is error free or not.

EXAMPLE 4

4. The Hamming bits appear in bits positions 1, 2, 4, 8 and 16. The following (16, 11) block check code is received at a receiver. Determine whether the data is error free or not.

EXAMPLE 5

How many Hamming bits would be added to a data block containing 128 bits?

USAGE OF HAMMING CODE

Hamming coding is only of use as a source code as a computer program to compress the characters. As a result it is only carried out in the front-end processor.

ADVANTAGE OF HAMMING CODE

Extremely effective on networks where the data streams are prone to single-bit errors.

DISADVANTAGE OF HAMMING CODE

Single-bit detection and correction code, if multiple bits are errored then the errors are detected but the resultant could cause another bit that is correct to be changed, causing the data to be further errored.

EXAMPLE 6

5. An (11,7) block check code is received. The Hamming bits are in bit positions 1, 2, 4 and 8. Determine whether the data is errored and which bit or bits are errored.

HAMMING DISTANCE

The number or bit position in which two codeword differs.

Required Hamming distance for error detection:

Hd = d + 1Required Hamming distance for error ccorrection:

Hd = 2d + 1

EXAMPLE

Calculate the Hamming distance to detect and correct 3 single-bit errors that occurred during transmission. Also compute for the number of Hamming bits for a 23 bit data string.

SYNCHRONIZATION

SYNCHRONIZE

- means to coincide or agree in time

SYNCHRONIZATION

4 TYPES OF SYNCHRONIZATION

1. Bit or Clock Synchronization - ensures that the transmitter and

receiver agree on a precise time slot for the occurrence of a bit

SYNCHRONIZATION

4 TYPES OF SYNCHRONIZATION

2. Modem or Carrier Synchronization

SYNCHRONIZATION

4 TYPES OF SYNCHRONIZATION

3. Character Synchronization

- identifying the beginning and the end of a character code

SYNCHRONIZATION

4 TYPES OF SYNCHRONIZATION

a. asynchronous data format - each character is framed between a start and a stop bit

idle line – no data transmission; data communication circuit is identified by the transmission of continuous 1’s

EXAMPLE 1

For the following string of asynchronous ASCII-encoded data, identify each character (assume even parity and 2 stop bits ).

EXAMPLE 2

For the following string of asynchronous ASCII-encoded data, identify each character (assume even parity and 2 stop bits ).

EXAMPLE 3

The following asynchronous data stream is received at an RS232C port. The data has a single start bit and two stop bits. A parity bit is incorporated with each character.

Determine the binary code.

EXAMPLE 4

The following asynchronous data stream is received at an RS232C port. The data has a single start bit and two stop bits. A parity bit is incorporated with each character.

65EABCE7 - hexadecimal

Determine the binary code.

SYNCHRONIZATION

4 TYPES OF SYNCHRONIZATION

b. synchronous data format - rather than frame each character independently with start and stop bits, s unique synchronizing character called a SYN character is transmitted at the beginning of each message.

EXAMPLE 1

For the following string of synchronous ASCII-encoded data, identify each character (assume odd parity ).

4. Message Synchronization

FOR YOUR INFORMATION

- To detect d single-bit errors, you need a Hamming distance of d + 1 code because with such a code there is no way that d single bit errors can change a valid codeword into another valid codeword.

- Similarly, to correct d single-bit errors, you need a distance 2d + 1 code because that way the legal codeword are so far apart that even with d changes. The original codeword is still closer than any other codeword.

- Hamming codes can only correct single bit errors. However there is a trick that can be used to permit Hamming codes to correct burst errrors.

MARAMING SALAMAT

GID SA PAKIKINIG!!!!!!!

ASSIGNMENT

Answer #s 2-1 to 2-4 problems; Advanced Electronic Communications Systems; 2nd edition by Wayne Tomasi

SEATWORK

Code each ASCII character in the word “dYoSa” for transmission over an asynchronous link where one start bit, a parity bit and two stop bits are employed. Assume even parity.