On the Theory of Low-Density Convolutional Codes

On Low-Density Parity-Check Convolutional Codes

Abstract – In this paper a formal theory, construction methods, and a random ensemble approach for low-density parity-check convolutional codes (including turbo-codes) are presented. The principles of iterative decoding of low-density parity-check (LDPC) convolutional codes are given, and an iterative algorithm for decoding of homogeneous LDPC convolutional codes is described. Some simulation r...

On the theory of low-density parity-check convolutional codes II

Type-III LDPC Convolutional Codes

A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

A Construction for Low Density Parity Check Convolutional Codes Based on Quasi-Cyclic Block Codes

A set of convolutional codes with low density parity check matrices is derived from a class of quasi-cyclic low density parity check block codes. Their performance when decoded using the belief propagation algorithm is investigated.

Convolutional Cylinder-type Block-circulant Cycle Codes

In this paper, we consider a class of column-weight two quasi-cyclic low-density parity check codes in which the girth can be large enough, as an arbitrary multiple of 8. Then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. Finally, we show that the free distance of the convolutio...