Parallel‐in encoding of quasi‐cyclic low‐density parity‐check codes

Algebraic structure of quasicyclic codes

We use Gr1 obner bases of modules as a tool in the construction and classi2cation of quasicyclic codes. Whereas previous studies have been mainly concerned with the 1-generator case, our results elucidate the structure of arbitrary quasicyclic codes and their duals. As an application we provide a complete characterisation of self-dual quasicyclic codes of index 2. ? 2001 Elsevier Science B.V. A...

Dft Characterization of Minimal Quasicyclic Codes

Encoding Subsystem Codes

In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the known results on encoding of stabilizer codes. Along the way we also show how Clifford codes can be encoded. We also show that gauge qubits can be exploited to...

The homogeneous weight for $R_k$, related Gray map and new binary quasicyclic codes

Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family Rk, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We find an associated Gray map for the homogeneous weight using first order Reed-Muller codes and we describe some of the general properties of the images of code...

Convolutional Codes: Construction and Encoding

This chapter introduces a widely used class of codes, called convolutional codes, which are used in a variety of systems including today’s popular wireless standards (such as 802.11) and in satellite communications. They are also used as a building block in more powerful modern codes, such as turbo codes, which are used in wide-area cellular wireless network standards such as 3G, LTE, and 4G. C...