| Reed-Solomon.... The Codes | |||||||||||||||
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| Some Introduction Info You Need To Know | |||||||||||||||
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The
basic concept is to add redundancy to a message in order to eliminate the
needfor retransmission of the data. It was found that dramatic gains in
performance could be achieved by intelligently adding redundancy to a message.
Thisaddition of redundancy to the message is called Forward Error Correction
(FEC). There are many methods of adding redundancey to a message, but one
of the mostefficient and popular methods is Reed-Solomon coding. The multiple-error-correcting
capability of RS codec has been used in many practical applications, includingmagnetic
and optical storage systems, space and mobile communications, etc.. It
is important to be familiar with some of the terminology for describing
Reed-Solomon codes. The mathematics underlying RS codes is very involved
andbeyond the scope of this paper. A Reed-Solomon code is described as
an (n,k) code, where the codewords consist of n symbols of which k are
message symbols.The following parameters are important in the characterization
of the codes: m = the number of bits per symbol n = the code length in
symbols k = the uncoded message lengh in symbols (n-k) = the number of
check symbols t = the maximum number of symbol errors that can be corrected
(half of (n-k)) Designing RS codecs is very difficult. Knowledge of RS
codes is highly specialized and not within the mainstream designers' domain
of expertise. This isbecause RS codes operate over an algebraic finite
field called Galios Field, and the encoding and decoding algorithms are
complicated. To understand the complexity of thecoding theory, this report
will not address the theoretical aspects of the algorithms but will focus
in the implementation. There are a large number of available codingalgorithms
and techniques for carrying out the finite field arithmetic [Blahut83].
It's unclear which approach is the best for any given application. Anotherconsideration
is that the m-bit finite field elements can processed in series or in parallel.
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| An Easier Explanation (the example)! | |||||||||||||||
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The
RS code has k information symbols (rather than bits), r parity symbols
and a total codeword length of n (= k+r) symbols. Tbe number of symbols in the codeword is given by n = 2m - 1 The code is able to correct errors in t symbols where t = r/2 Example If the number of bits in a symbol is 8 (m=8), then number of symbols in a codeword is n = 28 - 1 = 255. Also, t is selected as 16 which means that r = 2t = 32. Then k = n - r = 255 - 33 = 223 information symbols per codeword. The code rate Rc is given by Rc = k/n = 223/255 = 7/8 The total number of bits in a codeword will be 255 x 8 = 2040 bits per codeword. Since the RS code can correct sixteen symbols, it can correct a burst of 16 x 8 = 128 consecutive bit errors. However, the code under consideration, must have an error-free region of 255 - 16 = 239 symbols after every 128 consecutive bit errors corrected. This is a disadvantage of Reed-Solomon RS) code and severely limits the use of this technique of data coding. |
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| Extras | |||||||||||||||
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Reed-Solomon Codes are made up basically in 0s and 1s. This makes it easier
to follow. During my information search on how exactly to decode and encode
these specail codes, I found that there is no way you can put all the informtion
on one homepage. You actually find can find all the codes if you search
under |
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