14-05-2014, 11:27 AM
VHDL IMPLEMENTATION OF REED – SOLOMON CODES
[attachment=63210]
ABSTRACT
Channel coding is used for providing reliable information through the transmission channel to
the user .It is an important operation for the digital communication system transmitting digital
information over a noisy channel. Channel coding can use either Automatic Repeat request or
Forward Error Correction technique depending on the properties of the system or on the
application in which the error correcting is to be introduced.
Error – control coding techniques are based on the addition of redundancy to the information
message according to a prescribed rule thereby providing data a higher bit rate. This
redundancy is exploited by decoder at the receiver end to decide which message bit was
actually transmitted. The combined goal of the channel encoder and the decoder is to minimize
the channel noise. Block codes and convolutional codes are two main methods to introduce
error – correcting codes.
INTRODUCTION
Digital communication system is used to transport an information bearing signal from the
source to a user destination via a communication channel. The information signal is processed
in a digital communication system to form discrete messages which makes the information
more reliable for transmission. Channel coding is an important signal processing operation for
the efficient transmission of digital information over the channel. It was introduced by Claude
E. Shannon in 1948 by using the channel capacity as an important parameter for error - free
transmission. In channel coding the number of symbols in the source encoded message is
increased in a controlled manner in order to facilitate two basic objectives at the receiver: error
detection and error correction.
Error detection and error correction to achieve good communication is also employed in
electronic devices. It is used to reduce the level of noise and interferences in electronic
medium. The amount of error detection and correction required and its effectiveness depends
on the signal to noise ratio (SNR).
ERROR CONTROL CODING
INTRODUCTION
The designer of an efficient digital communication system faces the task of providing a system
which is cost effective and gives the user a level of reliability. The information transmitted
through the channel to the receiver is prone to errors. These errors could be controlled by using
Error- Control Coding which provides a reliable transmission of data through the channel. In
this chapter, a few error control coding techniques are discussed that rely on systematic
addition of redundant symbols to the transmitted information. Using these techniques, two
basic objectives at the receiver are facilitated: Error Detection and Error Correction.
CONCURRENT ERROR DETECTION SCHEMES
Schemes for Concurrent Error Detection (CED) find wide range of applications, since only
after the detection of error, can any preventive measure be initiated. The principle of error
detecting scheme is very simple, an encoded codeword needs to preserve some characteristic of
that particular scheme, and a violation is an indication of the occurrence of an error. Some of
the CED techniques are discussed below.
DEFINITION OF GALOIS FIELD
A Finite Field is a field with a finite field order (i.e., number of elements), also called a Galois
field. The order of a finite field is always a prime or a power of a prime . For each prime
power, there exists exactly one finite field GF(p m ).A Field is said to be infinite if it consists of
infinite number of elements, for e.g. Set of real numbers, complex numbers etc. Finite field on
the other hand consist of finite number of elements.
ADDITION/SUBTRACTION
Generally the field GF (2 m ) represents a set of integers from zero to 2 m - 1. Addition and
subtraction of elements of GF(2 m ) are simple XOR operations of the two operands. Each of the
elements in the GF is first represented as a corresponding polynomial. The addition or
subtraction operation is then represented by the XOR operation of the coefficient of
corresponding polynomials. However since the more complex operations are extensively used
in RS encoding and decoding algorithms, the development of their hardware structures have
received considerable attention.
Note that GFA does not distinguish between addition and subtraction operations; both are
considered as XOR operations. Since both operations follow modulo arithmetic, the result
always evaluates to a value within the field.
CONCLUSION
In this thesis, error detection and correction techniques have been used which are essential for
reliable communication over a noisy channel. The effect of errors occurring during
transmission is reduced by adding redundancy to the data prior to transmission. The
redundancy is used to enable a decoder in the receiver to detect and correct errors. Cyclic
Linear block codes are used efficiently for error detection and correction. The encoder splits
the incoming data stream into blocks and processes each block individually by adding
redundancy in accordance with a prescribed algorithm. Likewise, the decoder processes each
block individually and it corrects errors by exploiting the redundancy present in the received
data. An important advantage of cyclic codes is that they are easy to encode. Also they posses a
well defined mathematical structure which has lead to very efficient decoding schemes for
them.
[attachment=63210]
ABSTRACT
Channel coding is used for providing reliable information through the transmission channel to
the user .It is an important operation for the digital communication system transmitting digital
information over a noisy channel. Channel coding can use either Automatic Repeat request or
Forward Error Correction technique depending on the properties of the system or on the
application in which the error correcting is to be introduced.
Error – control coding techniques are based on the addition of redundancy to the information
message according to a prescribed rule thereby providing data a higher bit rate. This
redundancy is exploited by decoder at the receiver end to decide which message bit was
actually transmitted. The combined goal of the channel encoder and the decoder is to minimize
the channel noise. Block codes and convolutional codes are two main methods to introduce
error – correcting codes.
INTRODUCTION
Digital communication system is used to transport an information bearing signal from the
source to a user destination via a communication channel. The information signal is processed
in a digital communication system to form discrete messages which makes the information
more reliable for transmission. Channel coding is an important signal processing operation for
the efficient transmission of digital information over the channel. It was introduced by Claude
E. Shannon in 1948 by using the channel capacity as an important parameter for error - free
transmission. In channel coding the number of symbols in the source encoded message is
increased in a controlled manner in order to facilitate two basic objectives at the receiver: error
detection and error correction.
Error detection and error correction to achieve good communication is also employed in
electronic devices. It is used to reduce the level of noise and interferences in electronic
medium. The amount of error detection and correction required and its effectiveness depends
on the signal to noise ratio (SNR).
ERROR CONTROL CODING
INTRODUCTION
The designer of an efficient digital communication system faces the task of providing a system
which is cost effective and gives the user a level of reliability. The information transmitted
through the channel to the receiver is prone to errors. These errors could be controlled by using
Error- Control Coding which provides a reliable transmission of data through the channel. In
this chapter, a few error control coding techniques are discussed that rely on systematic
addition of redundant symbols to the transmitted information. Using these techniques, two
basic objectives at the receiver are facilitated: Error Detection and Error Correction.
CONCURRENT ERROR DETECTION SCHEMES
Schemes for Concurrent Error Detection (CED) find wide range of applications, since only
after the detection of error, can any preventive measure be initiated. The principle of error
detecting scheme is very simple, an encoded codeword needs to preserve some characteristic of
that particular scheme, and a violation is an indication of the occurrence of an error. Some of
the CED techniques are discussed below.
DEFINITION OF GALOIS FIELD
A Finite Field is a field with a finite field order (i.e., number of elements), also called a Galois
field. The order of a finite field is always a prime or a power of a prime . For each prime
power, there exists exactly one finite field GF(p m ).A Field is said to be infinite if it consists of
infinite number of elements, for e.g. Set of real numbers, complex numbers etc. Finite field on
the other hand consist of finite number of elements.
ADDITION/SUBTRACTION
Generally the field GF (2 m ) represents a set of integers from zero to 2 m - 1. Addition and
subtraction of elements of GF(2 m ) are simple XOR operations of the two operands. Each of the
elements in the GF is first represented as a corresponding polynomial. The addition or
subtraction operation is then represented by the XOR operation of the coefficient of
corresponding polynomials. However since the more complex operations are extensively used
in RS encoding and decoding algorithms, the development of their hardware structures have
received considerable attention.
Note that GFA does not distinguish between addition and subtraction operations; both are
considered as XOR operations. Since both operations follow modulo arithmetic, the result
always evaluates to a value within the field.
CONCLUSION
In this thesis, error detection and correction techniques have been used which are essential for
reliable communication over a noisy channel. The effect of errors occurring during
transmission is reduced by adding redundancy to the data prior to transmission. The
redundancy is used to enable a decoder in the receiver to detect and correct errors. Cyclic
Linear block codes are used efficiently for error detection and correction. The encoder splits
the incoming data stream into blocks and processes each block individually by adding
redundancy in accordance with a prescribed algorithm. Likewise, the decoder processes each
block individually and it corrects errors by exploiting the redundancy present in the received
data. An important advantage of cyclic codes is that they are easy to encode. Also they posses a
well defined mathematical structure which has lead to very efficient decoding schemes for
them.