implementation of hamming code in verilog ppt
#1

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#2
Implementation of Hamming code using VLSI
I. INTRODUCTION
One of the major issues in the field of communication is the
secure and error free transmission of data from transmitter to
receiver. And for error free transmission there are number of
technologies. One of the technologies which is used for
correcting forward error is the Hamming code technology.
Around 1947 Richard W. Hamming developed this
technology to detect and correct single bit errors in
transmitted data. In Hamming code error detection and
correction technique to get error free data at destination, we
encrypt information data according to even and odd parity
method before transmission of information at source
end.[3][1]
In telecommunication, Hamming codes are a family of linear
error correcting codes. Hamming codes can detect upto two
and correct upto one bit errors. By contrast the simple parity
code cannot correct errors, and can detect only odd number of
errors. Hamming code are special in that they are perfect
codes, that is they achieve the hightest possible rate for codes
with their block length and minimum distance. Because of the
simplicity of hamming codes, they are widely used in
computer memory. In this context one often uses an extended
hamming code with one extra parity bit. Extended hamming
code achieve a distance of 4, which allows the decoder to
distinguish between the situation in which at most one bit
error occurred and the situation in which two bit error
occurred. In this sense, extended hamming codes are single
error correcting and double-error detecting and often reffered
to as SECDED.[3][4]
In this paper we have written Verilog code for finding error
location and correct the bit which is corrupted. At the
destination, we receive 7-bit of data with 4 redundancy bits.
This received data may be corrupted due to noise. To remove
this noise we find the address of the error bit then correct
them. To find the location of error bit and correct them we
write code in Verilog language.This paper is organized as
follows: the concept of hamming code along with the
application of it, Verilog language, Why Verilog is preffered
over VHDL, Implementation of hamming code, Performance
and experimental results, conclusion and references.
II. HAMMING CODE
Hamming code are the linear block code which are invented
by Richard.W. Hamming. They are an improvement over
simple parity code method. Hamming codes are valid only
when the hamming distance between the bits is less then or
equal to one. By contrast, the simple parity code cannot
correct errors, and can only detect an odd number of errors.
They are the type of binary codes. The idea of hamming
distance is the central concept in coding the error control. The
hamming distance between the two words (of the same size)
is the number of differences between the corresponding
bits.The hamming distance can easily be found if we apply the
Xor operation on the two words and count the number of 1s in
the result. The hamming distance is a value always greater
then zero. If we find the hamming distance between any two
words it will be the result of the Xoring of the two bits. Like
the hamming distance between d (000,011) is 2 because 000
xor 011 is 011(two 1s) and the hamming distance between
d(10101,11110) is 3 because 10101 xor 11110 is 01011(three
1s).[3][7]
Hamming code method works only on two methods(even
parity, odd parity) for generating redundancy bits. The number
of redundancy bits are generated using a formula. The number
of redundancy depends on the number of information data
bits. The formula is:
2^r = D+r+1………………………………………………...(1)
Here, r = number of redundancy bits
D = number of information data bits
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#3

In mathematics, digital communication and information theory, error detection and correction has great practical importance in maintaining information integrity across noisy channels. Error coding is considered as a method of detecting and correcting these errors to ensure that the information is transferred intact from its source to its destination. There are various error correcting techniques to detect and correct the error. One of the popular techniques based on forward error correction is hamming code. This paper focuses on design and its hardware implementation on Field programmable Gate Array (FPGA).
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