Free Distance and Error Distribution
The free distance (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
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 code with an inner convolutional code. The popular solution for this problem is to interleave data before convolutional encoding, so that the outer block (usually Reed-Solomon) code can correct most of the errors.
Read more about this topic: Convolutional Code
Famous quotes containing the words free, distance, error and/or distribution:
“A counterfeiting law-factory, standing half in a slave land and half in a free! What kind of laws for free men can you expect from that?”
—Henry David Thoreau (1817–1862)
“Why does the past look so enticing to us? For the same reason why from a distance a meadow with flowers looks like a flower bed.”
—Franz Grillparzer (1791–1872)
“It is not to everyone’s taste that truth should be pronounced pleasant. But at least let no one believe that error becomes truth when it is pronounced unpleasant.”
—Friedrich Nietzsche (1844–1900)
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”
—Ralph Waldo Emerson (1803–1882)