Editing Convolutional code (section)

== Free distance and error distribution ==
[[File:Recnonrecber.png|thumb|right|300px|Theoretical bit-error rate curves of encoded QPSK (recursive and non-recursive, soft decision), additive white Gaussian noise channel. Curves are small distinguished due to approximately the same free distances and weights.]]

The '''free distance'''<ref>Moon, Todd K. "[https://leseprobe.buch.de/images-adb/7b/4f/7b4f94db-7c55-4836-9b61-2ff98cb242d9.pdf Error correction coding]." Mathematical Methods and Algorithms. Jhon Wiley and Son (2005).- p.508</ref> (''d'') is the minimal [[Hamming distance]] between different encoded sequences. The ''correcting capability'' (''t'') of a convolutional code is the number of errors that can be corrected by the code. It can be calculated as

:<math>t=\left \lfloor \frac{d-1}{2} \right \rfloor.</math>

Since a convolutional code doesn't use blocks, processing instead a continuous bitstream, the value of ''t'' applies to a quantity of errors located relatively near to each other. That is, multiple groups of ''t'' errors can usually be fixed when they are relatively far apart.

Free distance can be interpreted as the minimal length of an erroneous "burst" at the output of a convolutional decoder. The fact that errors appear as "bursts" should be accounted for when designing a [[Concatenated error correction code|concatenated code]] with an inner convolutional code. The popular solution for this problem is to [[Error correction code#Interleaving|interleave]] data before convolutional encoding, so that the outer block (usually [[Reed–Solomon error correction|Reed–Solomon]]) code can correct most of the errors.