Error correction

There are great many of the different error correction codes; consult the special literature. Reed-Solomon is only one of the families. If you provide an exact task statement, I could give you more meaningful advice.

As for the hard and fast methods, you can consider the following:

• break your data into the blocks of N bytes each

• append a CRC to each block

• insert a check block at every M blocks. The check block is a XOR of all blocks.

• Now, if any one of M blocks gets corrupt, you can recover it.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

Hi Vladimir,

Thank you for your reply.

As you say, your suggestion with the check block works only for max 1 faulty word. I need to support up to 40 faulty words (see original post). The number of words used to hold the encoded data is still to be chosen, but I would prefer something like 256 or higher (for storage efficiency).

In other words, I'd like to store ~150-216 words of data in 256 cells (for example), and be able to recover them even in presence of up to

40 faulty cells. The data words may be single bits, or bytes, or groups of bytes - I'd be equally happy with any of these.

Can you please point me to algorithms and literature that help me solve this problem efficiently?

Regards, Marc

No. That works up to one entirely faulty block.

I need to support up to 40 faulty words (see original

Asumming the error pattern is random, in general, you need two redundant words per every corrected word.

If each cell is one byte, then the RS code (255, 175) comes to mind. The decoder for such code is not very simple.

The data words may be single bits, or bytes, or

Classic book:

R. Blahut "The theory and practice of the error control codes"

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

Any book on error control coding has the information you need.

That's going to be true of any form of error control.

If the F locations are known up front, the error correction has solve F equations in F unkowns. If the locations are not known up front, it has to solve 2F equations in 2F unknowns. Obviously as the value of F increases, the time to solve the equations increases.

Any parameterizable Reed-Solomon implementation should work fine. There isn't anything special about your problem as stated.

Reed-Solomon is a code, not an algorithm. There are various algorithms for Reed-Solomon decoding, with various performance characteristics.

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