Tag Archives: reed solomon

Variable Length Reed-Solomon

Recently, someone had mentioned to me that the thing they liked most about convolutional codes was the ability to just send data in any amount.  With convolutional codes, an internal state determines what encoded bits to send.  This gives close … Continue reading

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Updated Reed-Solomon Encoder

When I originally wrote my Reed-Solomon encoder, I used the basic polynomial long division method directly.  This made a lot of sense at the time.  It turns out that there is actually a slightly better method.

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Xilinx’s ISIM and TCL

In Xilinx’s ISE 11, isim is another of the tools that was made by people who didn’t intend on using them.  At least, not in the way they would be advertised to the end user.  Really, the disconnect between the … Continue reading

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Reed Solomon Decoder, Forney’s Equation

In the previous articles, I described how to find the syndromes, the error locater polynomial, and the roots of that polynomial.  The last bit of information needed is the error magnitudes.  Forney’s equation can be used to determine this. 

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Reed Solomon Decoder, Chein Search

The Berlekamp-Massey algorithm provides an error locater polynomial.  Similar to the syndromes, this polynomial doesn’t provide the required information directly.  Instead, it is the multiplicative inverse of the roots of this polynomial that correspond to the error locations.  Just like … Continue reading

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Reed Solomon Decoder, Berlekamp-Massey

Given a sequence of syndromes, the Berlekamp-Massey algorithm determines an LFSR that could generate this sequence.  This helps explain how the syndromes can both find and correct errors.  The locations of errors are based on the pattern behind the syndromes.  … Continue reading

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Reed Solomon Decoder, Syndromes

As mentioned, the first part of my Reed-Solomon decoder implementation is the calculation of syndromes.  This is a straightforward process that only requires a large amount of parallel processing. 

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Reed Solomon Decoder, Overview

Recently, I had written a Reed-Solomon encoder module out of curiosity.  The next step was to write the decoder.  The resulting decoder was written to work with my encoder — allowing a valid input every cycle.  The project was very … Continue reading

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Reed-Solomon Encoder

This article describes how to make a performance optimized Reed-Solomon encoder.  The actual encoder is for an full-length, narrow-sense RS code.  In this case, the code generated was an code that could allow at least 8 bytes to be corrected, … Continue reading

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