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:

    None who have always been free can understand the terrible fascinating power of the hope of freedom to those who are not free.
    Pearl S. Buck (1892–1973)

    A petty reason perhaps why novelists more and more try to keep a distance from journalists is that novelists are trying to write the truth and journalists are trying to write fiction.
    Graham Greene (1904–1991)

    You can hardly convince a man of an error in a life-time, but must content yourself with the reflection that the progress of science is slow. If he is not convinced, his grandchildren may be. The geologists tell us that it took one hundred years to prove that fossils are organic, and one hundred and fifty more to prove that they are not to be referred to the Noachian deluge.
    Henry David Thoreau (1817–1862)

    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)