This dissertation considers block and convolutional codes in rank metric with the objective of designing and investigating efficient decoding algorithms for both code classes. This Reed–Solomon-like code class is based on the evaluation of linearized polynomials and is nowadays called Gabidulin codes. An optimal-cardinality algebraic code construction in rank metric was introduced some decades ago by Delsarte, Gabidulin and Roth. Rank-metric codes recently attract a lot of attention due to their possible application to network coding, cryptography, space-time coding and distributed storage. We derive a lower bound on the slope of any rate b/c convolutional code with a certain degree.

For the high pe regime, convolutional codes that have a good slope (the minimum normalized cycle weight) are seen to be good. For the low pe regime, convolutional codes with good distance properties show good performance. Simulations indicate that convolutional codes are required to possess different properties to achieve good performance in low pe and high pe regimes. In this work, we investigate the performance of CNECCs under the error model of the network where the edges are assumed to be statistically independent binary symmetric channels, each with the same probability of error pe(0 ≤ pe e should be so that only single edge network-errors need to be accounted for, thus reducing the complexity of evaluating the probability of error of any CNECC. Convolutional network-error correcting codes (CNECCs) are known to provide error correcting capability in acyclic instantaneous networks within the network coding paradigm under small field size conditions.

Ge networx e codes