LDPC convolutional codes have been shown to be capable of achieving the same capacity-approaching performance as LDPC block codes with iterative message-passing decoding. However, traditional means of comparing block and convolutional codes tied to the implementation complexity of trellisbased decoding are irrelevant for message-passing decoders. In this paper, we undertake a comparison of LDPC...

A new class of (2k, k, 1) convolutional codes is proposed based on the method that creating long codes by short ones in this paper, by embedding (2k, k) double loop cyclic codes in (2, 1, 1) convolutional codes. The structural mechanism of the codes is revealed by defining a state transition matrix and using algebraic method. It is then shown that the code structure is excellent in both proport...

In this paper, we suggest a new technique for LDPC parity-check matrix (H-matrix) generation and a corresponding decoding process. The key idea is to construct LDPC H-matrix by using a convolutional encoder. It is easy to have many different coderates from a mother code with convolutional codes. However, it is difficult to have many different coderates with LDPC codes. Constructing LDPC Hmatrix...

In this work the output-observability of convolutional codes is examined and a decoding algorithm for convolutional codes using linear algebra techniques is presented. Key–Words: Codes, linear systems, output-observability, generalized inverses.

The difference between block codes and convolutional codes is the encoding principle. In the block codes, the information bits are followed by the parity bits. In convolutional codes the information bits are spread along the sequence. That means that the convolutional codes map information to code bits not block wise, but sequentially convolve the sequence of information bits according to some ...

Convolutional codes over rings behave quite differently from convolutional codes over fields, but they are the ones best suited for phase modulation. This behavior depends strongly on the structure of the underlying ring. Some basic concepts about ring convolutional codes, in particular over Zpr , and their structural properties such as basicity, systematicity, non-catastrophicity and minimalit...

We are extending to linear recurrent codes, i.e., to time-varying convolutional codes, most of the classic structural properties of fixed convolutional codes. Those results are obtained thanks to a module-theoretic framework which has been developed in linear control.

In this paper we obtain a number of [70,35,12] singly even self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes). One of them is the first known code with parameters Beta=140 Gamma=0. All codes are not pure double circulant i.e. could not be represented in systematic form. Keywords—convolutional encoding, quasi-cyclic codes weight enumeratorg, double circulant

Low density parity check (LDPC) block codes have been shown to achieve near capacity performance for binary transmission over noisy channels. Block codes, however, require splitting the data to be transmitted into frames, which can be a disadvantage in some applications. Convolutional codes, on the other hand, have no such requirement, and are hence well suited for continuous transmission. In [...

For rate R = 1=2 convolutional codes with 16 states there exists a gap between Heller’s upper bound on the free distance and its optimal value. This correspondence reports on the construction of 16state, binary, rate R = 2=4 nonlinear trellis and convolutional codes having dfree = 8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, ra...