3
$\begingroup$

In error correction for example for Reed-Solomon codes there are computed syndromes for received data in decoding process. What is intuitively a syndrome (I don't mean the mathematical expression for it)?

$\endgroup$

1 Answer 1

4
$\begingroup$

The word syndrome was introduced into error-control coding theory and practice (by Hagelbarger) very early on. It is a term borrowed from medicine: a syndrome is a group of symptoms, e.g. stomachache, nausea, fever, lack of appetite, which together are diagnostic (or highly suggestive) of the presence of a specific disease or condition -- in this instance, appendicitis. Note that the presence of a single symptom is usually not considered diagnostic of a specific disease, it is the presence of the syndrome or a collection of symptoms. This notion in medicine is almost exactly mirrored in the error-control coding world. If the syndrome is identically zero (there are no symptoms whatsoever), nothing needs to be done, and the received word is accepted as correct (no disease is diagnosed and no treatment is prescribed). A nonzero syndrome indicates that the received word has errors in it (the presence of symptoms means that something is not right with the patient), and in most cases, the syndrome is also diagnostic of the locations of the errors and what needs to be done to correct them with the (Reed-Solomon) decoder substituting for the physician's thought processes (from syndrome, find the error locations and values) and actions such as prescribing medicines or performing surgery (correct the errors, fill in the erasures, etc.). In some cases, the fact that the syndrome is nonzero indicates the presence of errors but the decoder is not able to determine the error locations and values (and so is unable to correct the errors). This is called decoder failure. In even fewer cases, the syndrome indicates a specific error pattern as the most likely cause but in fact the actual error pattern is something else. Correcting what the decoder thinks is the error pattern introduces more errors into the received word, thus making it "wronger" than before, but this is not detectable at the receiver. This is not called decoder malpractice but decoder error or undetected error, and is, fortunately, a very rare event, much rarer than decoder failure.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.