Search results
Results from the WOW.Com Content Network
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file
A two-out-of-five code is an encoding scheme which uses five bits consisting of exactly three 0s and two 1s. This provides () = possible combinations, enough to represent the digits 0–9.
The packing radius of C is the largest value of s such that the set of balls of radius s centered at each codeword of C are mutually disjoint. From the proof of the Hamming bound, it can be seen that for = ⌊ ⌋, we have: s ≤ t and t ≤ r.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
The description above is given for what is now called a serially concatenated code. Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6]
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes , but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
Linearity guarantees that the minimum Hamming distance d between a codeword c 0 and any of the other codewords c ≠ c 0 is independent of c 0. This follows from the property that the difference c − c 0 of two codewords in C is also a codeword (i.e., an element of the subspace C), and the property that d(c, c 0) = d(c − c 0, 0). These ...
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.