Two-dimensional (2D) convolutional codes are a generalization of (1D) convolutional codes, which are suitable for transmission over an erasure channel. In this paper, we present a decoding algorithm for 2D convolutional codes over such a channel by reducing the decoding process to several decoding steps applied to 1D convolutional codes. Moreover, we provide constructions of 2D convolutional codes that are specially tailored to our decoding algorithm.

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method gives a competitive performance when solving this kind of problems.

The multidimensional 0–1 knapsack problem is a combinatorial optimization problem, which is NP-hard and arises in many fields of optimization. Exact as well as heuristic methods exist for solving this type of problem. Recently, a population-based artificial fish swarm algorithm was proposed and applied in an engineering context. In this paper, we present a binary version of the artificial fish swarm algorithm for solving multidimensional 0–1 knapsack problem. Infeasible solutions are made feasible by a decoding algorithm. We test the presented method with a set of benchmark problems and compare the obtained results with other methods available in literature. The tested method appears to give good results when solving these problems.