Which error correction could should I use for GF(32)

Question

I searched for comparisons between Reed-Solomon, Turbo and LDPC codes but they all seem to focus on efficiency. I'm more interested in commercial license of available libs, easiness and GF(32), i.e. a code with 32 symbols only (available Reed-Solomon implementations work for GF(256) and above).

Efficiency (speed) is not relevant. The messages are comprised of 24 symbols.

Can you provide a quick comparison on the most well-known Reed-Solomon, Turbo and LDPC codes for this case in which speed is not relevant?

Thanks.

Answer 1

Basically, Reed-Solomon is optimal, thus it means that you can exactly correct up to (n-k)/2 errors (k=length of your message, n=length of message + EC symbols), while TurboCodes and LDPC are near-optimal, meaning that you can correct up to (n-k-e)/2 where e is a small constant, so in ideal cases you are very close to (n-k)/2 (that's why it's called near-optimal, it's close to the Shannon limit). TurboCodes and LDPC have similar error correction power, and there are lots of variants depending on your needs (you can find lots of literature reviews or presentations).

What the different variants of LDPC or Turbocodes do is to optimize the algorithm to fit certain characteristics of the erasure channel (ie, the data) so as to reduce the constant e (and thus approaching the Shannon limit). So the best variant in your case depends on the details of your erasure channel. Also, to my knowledge, they are all in public domain now (maybe not yet for Turbocodes patents, but if not yet then they will soon).