Search results
Results from the WOW.Com Content Network
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.
Since the source is only 4 bits then there are only 16 possible transmitted words. Included is the eight-bit value if an extra parity bit is used (see Hamming(7,4) code with an additional parity bit).
As explained earlier, it can either detect and correct single-bit errors or it can detect (but not correct) both single and double-bit errors. With the addition of an overall parity bit, it becomes the [8,4] extended Hamming code and can both detect and correct single-bit errors and detect (but not correct) double-bit errors.
LDPC encoder. During the encoding of a frame, the input data bits (D) are repeated and distributed to a set of constituent encoders. The constituent encoders are typically accumulators and each accumulator is used to generate a parity symbol.
This book is mainly centered around algebraic and combinatorial techniques for designing and using error-correcting linear block codes. [ 1 ] [ 3 ] [ 9 ] It differs from previous works in this area in its reduction of each result to its mathematical foundations, and its clear exposition of the results follow from these foundations.
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).
The rate of a block code is defined as the ratio between its message length and its block length: = /. A large rate means that the amount of actual message per transmitted block is high.
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.