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 two-dimensional convolutional codes with finite support are considered, i.e., convolutional codes whose codewords have compact support indexed in N and take values in F, where F is a finite field. The main goal of this work is to analyze the (free) distance properties of this type of codes of rate 1/n and degree δ. We first establish an upper bound on the maximum possible distance...

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...

Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

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...

Using a new parity-check matrix, a class of convolutional codes with a designed free distance is introduced. This new class of codes has many characteristics of BCH block codes, therefore, we call these codes BCH convolutional codes.

Convolutional codes over rings are particularly suitable for representing codes over phase modulation signals. In order to develop a complete structural analysis of this class of codes, it is necessary to study rational matrices over rings, which constitutes the generator matrices (encoders) for such convolutional codes. Noncatastrophic, minimal, systematic and basic generator matrices are intr...

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 ...

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...

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...