The main issue of Reed-Solomon correction

Question

Is Reed-Solomon error correction being performed on an instance with a byte (or several deleted bytes)? For example, let's say this is Reed Solomon's code (12.8), so theoretically he should be able to correct 2 errors (or 4 erasures, if the position is known). But what happens if only 11 (or 10) bytes are received and no one knows which bytes were deleted? Will the Reed-Solomon correction error be fixed?

Thanks,
Ben

Answer 1

RS decoding for erasures requires the character position to “fall” or be lost. The kind of error you are talking about is due to phase distortion.

Answer 2

You can make it work by simply navigating to possible positions where the character may be missing and letting it fix your result, so let's assume that you get 10 characters:

1234567890 

Change the following values:

 ??1234567890 ?1?234567890 ?12?34567890 : 1??234567890 1?2?34567890 : 1234567890?? 

Each attempt is likely to give you some result, most of which are not what you want. But I would expect that there should be exactly one result with a minimum number of additional modifications, and this should be the one you want to use as the most likely to be the correct answer.

For example, if you correct the first three numbers from the above example, you can get the following result:

  v 361274567890 917234567890 312734569897 : ^ ^ 

For the first and third cases, you have additional corrections made outside the filling of two blanks (marked with v and ^), while in the second case you fill in only the missing items, and the remaining characters correspond to the uncorrected input, so I would choose answer 2 as most likely to be correct.

Clearly, the likelihood that this works depends on the presence of other errors. Unfortunately, I cannot give you a strict set of conditions under which this method will work for sure.

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Another thing you can do if your message is long enough is to use the rotation method to basically have some orthogonal RS codes that cover your data. That way, if you fail, you can recover it using another. This method, for example, is used on compact discs (CDs), where it is called CIRC .

Answer 3

No, Reed-Solomon cannot automatically fix cases where bits are missing, because, like most other FEC algorithms, it was intended only to fix -flips bits . If you know the position of the missing bits, you can superimpose your received signal on these positions so that RS can work normally.

However, if you do not know the position, you will need to use a different algorithm that supports bit insertion or deletion of bits as marker and watermark codes.

Also note that RS can be used not only to erase, but also to process noisy bits using Forney's syndrome .