Some aspects of the present disclosure generally use a parity check matrix comprising, for example, a first tier according to a high rate core graph and a second tier for HARQ transmissions to use pseudo cyclic low density parity check. A method and apparatus for decoding a (QC-LDPC) rate ...
To reduce decoding complexity, separating parity-check matrices with small number of rows are preferred. The minimum number of rows in a parity-check matrix separating a given maximum number of erasures is called the separating redundancy. Upper and lower bounds on the separating redundancies are ...
In at least one embodiment, a parity check matrix may be generated from a base graph. For example, in at least one embodiment, a parity check matrix is generated by replacing zero-valued entries with an all-zero matrix of dimensions Z×Z, and non-zero entries with a permutation matrix, ...
The construction of the parity-check matrix for the (4, 6, L) spatially coupled LDPC ensemble. Proof of Theorem 1. We first prove that any matrix H[T0,L−1] coupling from a structure HlT satisfying condition (3) is the parity-check matrix of a spatially coupled LDPC ensemble. Each ...
The extra bits are known as parity-check bits. For each code, a parity-check matrix, H, is defined; in order to be a valid one, for each code word, x, it must satisfy the parity-check constraint (modulo-2 operations), Hx=0. Take as an example the case of k=3 and N=6. The...
This paper proposes a hybrid technique that combines the “parity-check” with the “G-matrix” to reduce the computational complexity of BP decoder for polar codes. The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage ...
1.A parity check matrix generation method, comprising:generating a partial matrix H1of m rows and k columns and a unit matrix H2of m rows and m columns;determining positions of matrix elements “1” of each row of said partial matrix H1to satisfy conditions that, when any two rows containe...
Consider two parity check codes.Code I is generated by the rulex1=u1 x4=u1⊕u2x2=u2 x5=u1⊕u3x3=u3 x6=u2⊕u3 x7=u1⊕u2⊕u3 Code II is the same except that x6=u2. (1)Write down the generator matrix and parity check matrix for code I.(2)Write out a decoding table for code ...
Check matrix generation method, coding method, decoding method, communication apparatus, communication system, the encoder and decoder For example, providing a quasi-cyclic matrix canonical which gave regularity specific to the cyclic permutation matrices and are arranged in a row direction and a column...
for example, in matrix 700, the upper left submatrix 701 corresponds to the parity check syndromes for bit positions 0-11. When using Hamming coding, as described above, to generate the actual P0parity bit which is serially transmitted along with the 40 data bits in the 12-bit example, an...