We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used in similar circumstances in classical communication. In this article, we provide an efficient polynomial formalism for describing their stabilizer group, der...

In this paper, the performance of punctured convolutional codes of short constraint lengths is discussed. The punctured codes are used to provide error protection to a particular user in an asynchronous CDMA system. A perfect phase reference is assumed to be available throughout this paper. A slow fading Rician channel is assumed. Maximum likelihood decoding through a Viterbi algorithm is used ...

The multidimensional convolutional codes are an extension of the notion of convolutional codes (CCs) to several dimensions of time. This paper explores the class of twodimensional convolutional codes (2D CCs) and 2D tail-biting convolutional codes (2D TBCCs ), in particular, from several aspects. First, we derive several basic algebraic properties of these codes, applying algebraic methods in o...

This article studies the effects of applying convolutional codes to a wideband code-division multiple access (WCDMA) system that supports multirate users. The system is modeled following the WCDMA standards and the channel introduces noise, frequency-selective fading, and MAI. Rate one-half convolutional codes suggested in the third-generation (3G) standards are studied; we find that the error-...

SUMMARY In order to guarantee pairwise independence of codewords in an ensemble of convolutional codes it is necessary to consider time-varying codes. However, Seguin has shown [1] that the pairwise independence property is not strictly necessary when applying the random coding argument and on this basis he derives a new random coding bound for rate 1/n fixed convo-lutional codes [2]. In this p...

In this note we introduce the concept of group convolutional code. We make a complete classification of the minimal S 3-convolutional codes over the field of five elements by means of Jategaonkar's theorems .

Arikan’s Polar codes [1] attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper bounded by β < 1 2 . Since their discovery, many attempts have been made to improve the error exponent and the finite block-length performance, while keeping...

We investigate the notion of cyclicity for convolutional codes as it has been introduced in the papers [15, 18]. Codes of this type are described as submodules of F[z]n with some additional generalized cyclic structure but also as specific left ideals in a skew polynomial ring. Extending a result of [15], we show in a purely algebraic setting that these ideals are always principal. This leads t...