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 rank distance and its slope are defined. Upper bounds for the free rank distance and the slope of (P)UM codes in the sum rank metric are derived. The construction of PUM codes based on Gabidulin codes achieves the upper bound for the free rank distance.
Abstract. This paper presents an introduction to the theory of generalized concatenated codes. We consider the encoding and decoding procedures of both ordinary concatenatedcodes, and generalized concatenatedcodes where block codes are used as inner codes. We give the main parameters of these codes, and by means of examples, show that under the same conditions the latter outperforms the former with respect to minimum code distance. We also heuristically describe the generalized concatenated decoding procedure. Then we show how the generalized concatenated coding ideas can be applied to encoded memoryless modulation. Such construction is often referred to as a multilevel code in literature. We consider the multilevel codes from the standpoint of generalized concatenated codes and with the help of a simple example, show how encoding and decoding procedures can be camed out. Ordinary concatenated and generalized concatenated coding schemes are considered next, using inner convolutional codes or inner modulation with memory. With the help of examples, we analyze the distance properties of such constructions.
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