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Concatenated codes Mar20

Page history last edited by Silas 15 years ago

Concatenated codes

 

 

This article welcomes suggestions and amendments from others since the author of this article just presents what he thinks is right, and he might be wrong.

 

Fix n. We will use a binary symmetric channel n times to transmit n bits.

Firstly, choose a GV code with parameters Formula over the finite field GF(2)  for the inner code. There are Formula bits of messages in the GV code.

Secondly, choose a Reed-Solomon code with parameters Formula over the finite field Formula for the outer code.

 

By choosing the above parameters, we can transmit  Formula symbols over the finite field Formula for the overall code.

 

The encoding and decoding procedures are done as follows.

The source chooses Formula symbols over the finite field Formula to transmit. Encode the Formula symbols using the  Reed-Solomon code  to obtain a codeword of length Formula over the finite field Formula. Then, for each symbol in sequence of the Reed-Solomon code, convert it into a Formula-bit sequence and encode the resulting bit sequence using the GV code. Since the length of each bit sequence generated by the GV code is Formula, the total length of the overall sequence is n.

 

The decoder will first decode each chunk, which is encoded by GV code, to obtain  Formula symbols over the finite field Formula. After that, the decoder will use the Reed-solomon code to try to recover the Formula symbols.

 

The choice of d and Formula will determine the performance of the overall code against errors induced by the channel. More specifically, d and Formula will determine the minimum Hamming distance of the overall code.

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