Hence a significant amount of decoder reuse can be observed with puncturing techniques.
5.1.4 Reed-Solomon (RS) Codes
In 1960, Irving Reed and Gus Solomon introduced RS codes in their paper entitled, Polynomial Codes
over Certain Finite Fields [25]. RS codes are nonbinary cyclic codes which have burst error correcting
capabilities [26]. The nonbinary or code symbols consist of m-bit symbols. The notation used in
the RS code is (n,k) where n number of code symbols in the code word and k number of data
symbols to be encoded. The following relationship holds true
(5.60)
where m number of bits used to create a RS symbol and t is the symbol error correcting capability of
the code. This leads to mathematical operations that satisfy the rules of the finite fields known as Galois
Fields (GF). The number of parity bits is equal to n k and is equal to 2t. Alternatively we can write
(5.61)
An important point to make here is that codes satisfying this relationship are optimal for any code of
the same length and dimension. This is sometimes called maximal distance (MD) codes. Also, defining
the code minimum distance as dmin n k 1, then we can rewrite the error correcting capability as
(5.62)
What this error-correcting capability property shows us is that in order to correct t symbols we need
to have 2t parity symbols.
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