In this paper, we present a construction method of non-binary low-density parity-check (LDPC) convolutional codes. Our construction method is an extension of Felström and Zigangirov construction [1] for non-binary LDPC convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-reg...

Algebraic methods for the construction, design and analysis of series of convolutional codes using row or block structures of unit schemes are developed. The general methods lead to the construction and analysis of series and infinite series of types of convolutional codes and of codes with specific properties. Explicit examples are given and properties may be shown algebraically. Algebraic dec...

| New nested convolutional codes and rate-compatible punctured convolutional (RCPC) codes with high constraint lengths and wide range of code rates are presented. It is shown that these codes are almost as good as the existing optimum convolutional codes for the same rates. The eeects of varying the design parameters of the RCPC codes, i.e. the mother code rate, the puncturing period and the co...

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 and each degree . The c...

Abstract—The free distance of (n, k, l) convolutional codes has some connection with the memory length, which depends on not only l but also on k. To efficiently obtain a large memory length, we have constructed a new class of (2k, k, l) convolutional codes by (2k, k) block codes and (2, 1, l) convolutional codes, and its encoder and generation function are also given in this paper. With the he...

In this lecture we discuss construction of signals via a trellis. That is, signals are constructed by labeling the branches of an infinite trellis with signals from a small set. Because the trellis is of infinite length this is conceptually different than the signals created in the previous chapter. We the codes generated are linear (the sum of any two sequences is also a valid sequence) then t...

In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding and by the direct product code construction applied to algebraic geometry codes. The parameters of the new convolutional codes are better than or comparable t...

A general method for constructing convolutional codes from units in Laurent series over matrix rings is presented. Using group rings as matrix rings, this forms a basis for in-depth exploration of convolutional codes from group ring encodings, wherein the ring in the group ring is itself a group ring. The method is used to algebraically construct series of convolutional codes. Algebraic methods...

It has long been known that convolutional codes have a natural, regular trellis structure that facilitates the implementation of Viterbi's algorithm [30,10]. It has gradually become apparent that linear block codes also/]ave a natural, though not in general a regular, "minimal" trellis structure, which allows them to be decoded with a Viterbi-1ike algorithn] [2,31,22,11,27,14,12,16,24,25,8,15]....

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best” recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error p...