We show that the state complexity profile of a convolutional code is the same as that of the reciprocal of the dual code of in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given ( 1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many ( 1) binary conv...

In this paper, starting with a family of convolutional codes, we construct a new convolutional code and we introduce also necessary and sufficient conditions in order that the new convolutional code is MDS.

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...

Abstract — In this paper, we propose a novel method to construct low rate recursive convolutional codes. The ‘overall’ convolutional code has a block code and a simple recursive convolutional code as building blocks. The novelty of this type of convolutional code is that it uses coset leaders in order to distinguish the signals that originate from different states. Several of these codes are th...

In this paper, we propose a novel method to construct low rate recursive convolutional codes. The ‘overall’ convolutional code has a block code and a simple recursive convolutional code as building blocks. The novelty of this type of convolutional code is that it uses coset leaders in order to distinguish the signals that originate from different states. Several of these codes are then used to ...

A trellis code encoded by using the encoder of a convolutional code with a short constraint length followed by an additional processing unit is equivalent to a trellis code with a large constraint length. In 1993, Hellstern proposed a trellis coding scheme for which the processing unit consists of a delay processor and a signal mapper. With Hellstern’s scheme, trellis codes with large free dist...

Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we construct a large family of unit-memory MDS convolutional codes over Fq with flexible parameters. Compared with previous works, the field size q required to ...

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary clas...

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglementassisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary class...

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. Focus is put on the ubiquitous inner differential encoder (used in particular to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 re...