Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Efficient encoding of low-density parity-check codes
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
TS-LDPC Codes: Turbo-Structured Codes With Large Girth
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 |
In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method "label-and-decide." We prove that the "label-and-decide" method is applicable to Tanner graphs with a hierarchical structure--pseudo-trees--and that the resulting encoding complexity is linear with the code block length. Next, we define a second type of Tanner graphs--the encoding stopping set. The encoding stopping set is encoded in linear complexity by a revised label-and-decide algorithm--the "label-decide-recompute." Finally, we prove that any Tanner graph can be partitioned into encoding stopping sets and pseudo-trees. By encoding each encoding stopping set or pseudo-tree sequentially, we develop a linear complexity encoding method for general low-density parity-check (LDPC) codes where the encoding complexity is proved to be less than 4 ċ M ċ, (k - 1) where M is the number of independent rows in the parity-check matrix and k represents the mean row weight of the parity-check matrix.