Parity bitParity check matrix for single bit error correcting code based on algebraic coding theory can be generated from the parity bit vectors by an efficient algorithm supported with examples. The novelty of this algorithm is the simplicity in its implementation.D. Roy CHOUDHURY...
This MATLAB function returns an m-by-n parity-check matrix, h, for a Hamming code of codeword length n = 2m–1.
Generate a parity-check matrix,h, for a Hamming code of codeword length 7. The function uses the default primitive polynomial in GF(8) to create the Hamming code. h = hammgen(3) h =3×71 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 ...
The stopping redundancy of a code is defined as the minimum number of rows in a parity-check matrix such that the stopping distance is equal to the minimum distance of the code. From: Academic Press Library in Mobile and Wireless Communications, 2014 ...
where H is a parity check matrix for some Hamming code, and the quotient is a complete graph; Arithmetic completely regular codes RSCC of rate L/N is applied on each column of L bits, from which N-L parity check bits are obtained. Improved iterative decoding of network-channel codes for...
,v^N]) is satisfied where H is the parity check matrix of an LDPC code, then the algorithm terminates. Otherwise, it continues with the next iteration. 2.2. Trapping sets The term trapping set first proposed by Richardson [7] was defined as a specific set of VNs connected to some CNs ...
matrix of the plane as a generator matrix or as a parity-check matrix of a linear code, showing that the underlying geometry can be translated in metric properties of the corresponding codes. Generalizations of these constructions have been studied since the 70’s and are still the subject of...
It should be noted that any k linearly independent codewords can be used to form a generator matrix, so G is not unique for a given code. Another important property of block codes is systematicity, as defined in the following: Definition 2.2 A block code is said to be systematic if...
6.1 Simulated Annealing on a 2x3 Protograph . . . . . . . . . . . . . . . . 101 6.2 Simulated Annealing on a 4x8 Protomatrix . . . . . . . . . . . . . . . 102 6.3 Tree Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
A q-ary LDPC code is a linear block code defined as the null space of a sparse parity-check matrix H over a finite field of q elements that is denoted by GF(q), where q is a power of a prime. From: OFDM for Optical Communications, 2010 ...