Combinatorica
Error control systems for digital communication and storage
Error control systems for digital communication and storage
Analog MAP Decoder for (8, 4) Hamming Code in Subthreshold CMOS
ARVLSI '01 Proceedings of the 2001 Conference on Advanced Research in VLSI
Introduction to Coding Theory
IEEE Transactions on Information Theory - Part 1
The intractability of computing the minimum distance of a code
IEEE Transactions on Information Theory
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
Efficient encoding of low-density parity-check codes
IEEE Transactions on Information Theory
Minimum-distance bounds by graph analysis
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Quasicyclic low-density parity-check codes from circulant permutation matrices
IEEE Transactions on Information Theory
Approximately Lower Triangular Ensembles of LDPC Codes With Linear Encoding Complexity
IEEE Transactions on Information Theory
| Hi-index | 754.84 |
Low-density parity-check (LDPC) codes may be decoded using a circuit implementation of the sum-product algorithm which maps the factor graph of the code. By reusing the decoder for encoding, both tasks can be performed using the same circuit, thus reducing area and verification requirements. Motivated by this, iterative encoding techniques based upon the graphical representation of the code are proposed. Code design constraints which ensure encoder convergence are presented, and then used to design iteratively encodable codes, while also preventing 4-cycle creation. We show how the Jacobi method for iterative matrix inversion can be applied to finite field matrices, viewed as message passing, and employed as the core of an iterative encoder. We present an algebraic construction of 4-cycle free iteratively encodable codes using circulant matrices. Analysis of these codes identifies a weakness in their structure, due to a repetitive patteru in the factor graph. The graph supports pseudo-codewords of low pseudo-weight. In order to remove the repetitive pattern in the graph, we propose a recursive technique for generating iteratively encodable codes. The new codes offer flexibility in the choice of code length and rate, and performance that compares well to randomly generated, quasi-cyclic and extended Euclidean-geometry codes.