Partial) Unit Memory ((P)UM) codes provide a powerful possibility to construct convolutional codes based on block codes in order to achieve a high decoding performance. In this contribution, a construction based on Gabidulin codes is considered. This construction requires a modified rank metric, the so–called sum rank metric. For the sum rank metric, the free rank distance, the extended row ran...

We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions [5]. Moreover we give a classification of one-dimensional Convolutional Goppa Codes and propose a characterization of MDS codes of this type. Introduction One of the main problems in coding theory is the construction of codes with a large distance, such as so-called MDS c...

Digital mobile radio systems based on the pan-European standards GSM and DCS 1800 are using concatenated coding schemes consisting of an inner error correcting convolutional code and an outer error detecting block code to ensure an appropriate performance. An improvement of this performance was achieved by applying list generating algorithms supplying a list of possible convolutional decoded se...

Abst rac t Systematic recursive convolutional encoders have been shown to play a crucial role in the design and implementation ofparallel concatenated codes (“turbo codes77). We present here a canonical structure of minimal linear systematic rate k / n encoders and use it in the search for good constituent codes of parallel concatenated codes. Tables of the best encoders for various rates are a...

In this correspondence the error exponent and the decoding complexity of binary woven convolutional codes with outer warp and with binary convolutional codes as outer and inner codes are studied. It is shown that an error probability that is exponentially decreasing with the product of the outer and inner code memories can be achieved with a nonexponentially increasing decoding complexity.

In a previous correspondence,’ a decoding procedurewhich uses continued fractions and which is applicable to a wideclass of algebraic codes including Goppa codes was presented. Theefficiency of this method is significantly increased. The efficiency of the decoding method in the above corre-spondencel can be significantly increased. In the following, allreferences will be to ...

Recently, we proposed a new design technique to construct high-rate convolutional codes based on a structure formed by a block encoder and a simpler convolutional encoder [1]. The search technique was based on the optimization of the output weight enumerating function of the code. Here, we prove that every (n, n − 1) convolutional code can be reduced to this structure. Following this result and...

of the Dissertation An Analytical Packet Error Rate Prediction for Punctured Convolutional Codes and an Application to CRC Code Design

The performance in terms of bit-error probability of low-rate convolutional codes is addressed. The Heller bound on the free distance is revised and an alternative formulation is given. A discussion of the key parameters determining the code performance and how to obtain good codes is followed by a comparison of codes of various rates for a fixed constraint length. It is concluded that simply l...