Low Density Parity Check Codes(LDPC)
LDPC codes are linear block codes with a particular structure for the parity check matrix H,
The parity check matrix is used to decode linear block codes with generator matrix G.
Specifically, a (dv, dc) regular binary LDPC has a parity check matrix H with dv ones in each column and dc ones in each row, where dv and dc are chosen as part of the code word design and are small relative to the codeword length.
- Since the fraction of nonzero entries in H is small, the parity check matrix for the code has a low density, and hence the name low density parity check codes.
- Provided that the codeword length is long, LDPC codes achieve performance close to the Shannon limit
- LPDC codes tend to have relatively high encoding complexity but low decoding complexity
- LDPC decoding uses iterative techniques,which are related to Pearl’s belief propagation commonly used by the artificial intelligence community
- The decoding algorithm for LDPC codes can detect when a correct code word has been detected, which is not necessarily the case for turbo codes
LDPC codes includes :
- Finding capacity limits for codes
- Determining effective code designs
- Efficient encoding and decoding algorithms and expanding the code designs to include nonregular and nonbinary LDPC codes as well as coded modulation