in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

Maximum-distance separable (MDS) convolutional codes are characterized through the property that the free distance attains the generalized singleton bound. The existence of MDS convolutional codes was established by two of the authors by using methods from algebraic geometry. This correspondence provides an elementary construction of MDS convolutional codes for each rate k/n and each degree δ. ...

Several new families of multi-memory classical convolutional Bose-Chaudhuri-Hocquenghem (BCH) codes as well as families of unit-memory quantum convolutional codes are constructed in this paper. Our unit-memory classical and quantum convolutional codes are optimal in the sense that they attain the classical (quantum) generalized Singleton bound. The constructions presented in this paper are perf...

Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit constructions. Two families of quantum convolutional codes are derived from generalized Reed-Solomon codes and from ReedMuller codes. A Singleton bound for pure con...

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 ...

Constructions of (classical) convolutional codes and their corresponding properties have been presented in the literature [1, 3–8, 12, 15–20]. In [3], the author constructed an algebraic structure for convolutional codes. Addressing the construction of maximum-distance-separable (MDS) convolutional codes (in the sense that the codes attain the generalized Singleton bound introduced in [18, Theo...

When a convolutional code is used to provide forward error correction for packet data transmission, the standard performance measures of convolutional codes, i.e., bit error rate and first-event error rate, become less useful. Instead we are interested in the average probability of block (or packet) error. In this paper a modified transfer function approach is used to obtain a union bound on th...

Low-density parity-check (LDPC) codes, invented by Gallager [2], who described and analyzed a block variant of the codes, arouse great interest of researchers. These codes are widely used in practice since they can be decoded by using relatively simple iterative decoding algorithms. Several modifications of these codes are known, in particular, generalized LDPC codes [3]. In contrast to Gallage...

In this paper, we present a construction method of terminated non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an expansion of Felstrom and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary LDPC convolutional codes is also discussed. The proposed ratecompatible code is designed from one single ...