Convolutional Code - Free Distance and Error Distribution

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:

    Most men, even in this comparatively free country, through mere ignorance and mistake, are so occupied with the factitious cares and superfluously coarse labors of life that its finer fruits cannot be plucked by them. Their fingers, from excessive toil, are too clumsy and tremble too much for that.
    Henry David Thoreau (1817–1862)

    The distance between your place in the kitchen and Miss Vollard’s place in the dining room is considerable.
    Blake Edwards (b. 1922)

    Men have an extraordinarily erroneous opinion of their position in nature; and the error is ineradicable.
    W. Somerset Maugham (1874–1966)

    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)