meaning that theparity check matrixof an (n,k) LBCHis a matrix of rankn−kand dimensions (n−k)×nwhose null-space is ak-dimensional vector with its basis forming thegenerator matrixG. Example: Parity-check matrices for (n,1)repetition codeHrepand (n,n−1) single-parity check cod...
2.The generator matrix andcheck matrixof q-cyclic codes are discussed,and then the theory of rank distance codes can be studied expediently.讨论了q-循环码的生成矩阵和校验矩阵,从而可以方便地研究秩距离码的理论。 3.Although thecheck matrixof LDPC codes is sparse,the generator matrix is not.LDPC...
Systematic encoding for non-full row rank, quasi-cyclic LDPC parity check matricesEncoding is performed by putting a low-density parity-check (LDPC) generator matrix into partial quasi-cyclic form comprising an identity matrix, a parity generator matrix, a zero matrix and a remainder matrix. The...
An identification scheme based on parity check matrix of error-correcting codes over GF(2) was proposed in the paper "A New Paradigm for Public Key Identification" by J. Stern(1996), a new identification scheme based on parity check matrix of rank distance codes over GF(qN) (q is a prim...
Noun1.parity check- a system of checking for errors in computer functioning odd-even check,redundancy check confirmation,substantiation,verification,check- additional proof that something that was believed (some fact or hypothesis or theory) is correct; "fossils provided further confirmation of the evol...
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 ...
derived this result using random constructions of very large and sparse parity-check matrices. Because of these random constructions the performance of the codes was only guaranteed with high probability and there was also the practical disadvantage that the storage of a particular parity-check matrix...
The generator matrix and check matrix of q-cyclic codes are discussed,and then the theory of rank distance codes can be studied expediently. 讨论了q-循环码的生成矩阵和校验矩阵,从而可以方便地研究秩距离码的理论。 3. Although the check matrix of LDPC codes is sparse,the generator matrix is no...
where msis termed as the memory of the parity-check matrix and Hi(t), where i=0, 1, . . . , ms, are (c−b)×c submatrices with full rank. A LPDCCC is periodic with period T if Hi(t)=Hi(t+T) for all i=0, 1, . . . , ms. If T=1, the code is time-invariant;...
LDPC (Low Density Parity Check) codes with corresponding parity check matrices selectively constructed with CSI (Cyclic Shifted Identity) and null sub-matrices. An LDPC matrix corresponding to an LDPC code is employed within a communication device to encode and/or decode coded signals for use in ...