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:
“I anticipate with pleasing expectations that retreat in which I promise myself to realize, without alloy, the sweet enjoyment of partaking, in the midst of my fellow citizens, the benign influence of good laws under a free government, the ever favorite object of my heart, and the happy reward, as I trust, of our mutual cares, labors, and dangers.”
—George Washington (1732–1799)
“Honor the spirits, but keep your distance from them.”
—Chinese proverb.
Confucian Analects.
“In religion,
What damned error but some sober brow
Will bless it, and approve it with a text,
Hiding the grossness with fair ornament?”
—William Shakespeare (1564–1616)
“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)