Error Control Coding, Second Edition
Error Control Coding, Second Edition
Low-complexity high-speed decoder design for quasi-cyclic LDPC codes
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
LDPC block and convolutional codes based on circulant matrices
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Capacity-approaching codes: can they be applied to the magnetic recording channel?
IEEE Communications Magazine
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The parity-check matrix of a non-binary low-density parity-check (LDPC) code over GF(q) is constructed by assigning non-zero elements from GF(q) to the 1s in that of the corresponding binary LDPC code. In this paper, we provide a theorem that establishes a necessary and sufficient condition that a q-ary matrix constructed by assigning non-zero elements from GF(q) to the 1s in the parity-check matrix of a binary quasi-cyclic LDPC code must satisfy in order for its null-space to define a non-binary quasi-cyclic LDPC (NB-QC-LDPC) code over GF(q). We then propose a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes that might serve better for different design goals. We also demonstrate that NB-QC-LDPC codes are very suitable for high-rate applications, e.g. applications in magnetic recording and storage systems and optical communication systems.