Abstract—A new class of (2k, k, 1) convolutional codes is proposed based on the method that creating long codes by short ones in this paper, by embedding (2k, k) double loop cyclic codes in (2, 1, 1) convolutional codes. The structural mechanism of the codes is revealed by defining a state transition matrix and using algebraic method. It is then shown that the code structure is excellent in both proportionality and diversity, so a superior code is easy to be obtained. Simulation results show that, the new convolutional codes present advantages over the traditional (2, 1, l) codes in the error-correcting capability and decoding speed.

Index Terms—convolutional codes, state transition matrix, magic square, viterbi decoding