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:
“You only have power over people so long as you don’t take everything away from them. But when you’ve robbed a man of everything he’s no longer in your power—he’s free again.”
—Alexander Solzhenitsyn (b. 1918)
“Are we not madder than those first inhabitants of the plain of Sennar? We know that the distance separating the earth from the sky is infinite, and yet we do not stop building our tower.”
—Denis Diderot (1713–1784)
“Custom calls me to’t.
What custom wills, in all things should we do’t,
The dust on antique time would lie unswept,
And mountainous error be too highly heaped
For truth to o’erpeer.”
—William Shakespeare (1564–1616)
“My topic for Army reunions ... this summer: How to prepare for war in time of peace. Not by fortifications, by navies, or by standing armies. But by policies which will add to the happiness and the comfort of all our people and which will tend to the distribution of intelligence [and] wealth equally among all. Our strength is a contented and intelligent community.”
—Rutherford Birchard Hayes (1822–1893)