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:
“He writes free verse, I’m told, and he is thought
To be the author of the Seven Freedoms:
Free Will, Trade, Verse, Thought, Love, Speech, Coinage.”
—Robert Frost (1874–1963)
“The distance that the dead have gone
Does not at first appear—
Their coming back seems possible
For many an ardent year.”
—Emily Dickinson (1830–1886)
“For my part I do, qua lay physicist, believe in physical objects and not in Homer’s gods; and I consider it a scientific error to believe otherwise.”
—Willard Van Orman Quine (b. 1908)
“The question for the country now is how to secure a more equal distribution of property among the people. There can be no republican institutions with vast masses of property permanently in a few hands, and large masses of voters without property.... Let no man get by inheritance, or by will, more than will produce at four per cent interest an income ... of fifteen thousand dollars] per year, or an estate of five hundred thousand dollars.”
—Rutherford Birchard Hayes (1822–1893)