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In the recent history of the theory of network coding the multi-shot network coding has been prove as a good alternative for the classical one-shot network theory which is managed by using block codes. To perform communications in this multi-shot context we have, among others, rank-metric convolutional codes and concatenated codes (using a convolutional code as an outer code and a rank-metric code as inner code). In this work we analyse their performance over the rank deficiency channel (described by Gilbert-Elliot channel model) in terms of the correction capabilities and the complexity of the two decoding schemes. published

The minimum distance of a code is an important measure of robustness of the code since it provides a means to assess its capability to protect data from errors. Several types of distance can be defined for convolutional codes. Column distances have important characterizations in terms of the generator matrices of the code, but also in terms of its parity check matrices if the code is noncatastrophic. The chapter presents the most important known constructions for maximum distance separable convolutional codes. There are natural connections to automata theory and systems theory, and this was first recognized by J. L. Massey and M. K. Sain in 1967. These connections have always been fruitful in the development of the theory on convolutional codes; the reader might also consult the survey. The chapter also presents decoding techniques for convolutional codes. It describes the decoding of convolutional codes over the erasure channel, where simple linear algebra techniques are applied. published

Maximum distance profile codes over finite nonbinary fields have been introduced and thoroughly studied in the last decade. These codes have the property that their column distances are maximal among all codes of the same rate and degree. In this paper, we aim at studying this fundamental concept in the context of convolutional codes over a finite ring. We extensively use the concept of p-encoder to establish the theoretical framework and derive several bounds on the column distances. In particular, a method for constructing (not necessarily free) maximum distance profile convolutional codes over Z_{p^r} is presented. published

A new construction of maximum rank distance systematic rank metric convolutional codes is presented, which permits to reduce the computational complexity of the decoding procedure, i.e., of the underlying Viterbi algorithm. This result is achieved by lowering the number of branch metrics to be calculated and by setting to the highest value the metric of the remaining edges in the trellis. published