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:
“The English people believes itself to be free; it is gravely mistaken; it is free only during election of members of parliament; as soon as the members are elected, the people is enslaved; it is nothing. In the brief moment of its freedom, the English people makes such a use of that freedom that it deserves to lose it.”
—Jean-Jacques Rousseau (1712–1778)
“No doubt, the short distance to which you can see in the woods, and the general twilight, would at length react on the inhabitants, and make them savages. The lakes also reveal the mountains, and give ample scope and range to our thought.”
—Henry David Thoreau (1817–1862)
“Meanwhile, if the fear of falling into error sets up a mistrust of Science, which in the absence of such scruples gets on with the work itself, and actually cognizes something, it is hard to see why we should not turn round and mistrust this very mistrust.... What calls itself fear of error reveals itself rather as fear of the truth.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Classical and romantic: private language of a family quarrel, a dead dispute over the distribution of emphasis between man and nature.”
—Cyril Connolly (1903–1974)