On Woven Convolutional Codes

Concatenation of several conventional convolutional encoders is a both powerful and practical method to obtain encoding schemes that are attractive for use in communication systems where very low error probabilities are needed. This thesis is devoted to woven convolutional codes, a construction where the constituent codes are woven together in a manner that resembles the structure of a fabric. A family of active distance measures for convolutional codes is defined. It is shown that the error correcting capability of a convolutional code is determined by the active distances. Lower bounds on the active distances are derived for the ensemble of periodically time-varying convolutional codes. The simplest construction of serially concatenated convolutional codes is considered, viz., a direct cascade of two convolutional encoders. Important structural properties for the cascaded convolutional encoder is shown both for the case of matched and for unmatched rates. Several interesting examples of cascaded convolutional codes are considered and examined. Lower bounds on the active distances and the free distance are derived for the ensemble of periodically time-varying cascaded convolutional codes. Woven convolutional codes can be viewed as a generalization of cascaded convolutional codes. The general construction is called the twill and it is described together with two important special cases, viz., woven convolutional codes with outer and inner warp. The woven convolutional encoder inherits many of its structural properties, such as minimality, from the constituent encoders. Distance properties for the constructions are examined and upper and lower bounds on the free distance are derived. Decoding of woven convolutional codes should be performed iteratively and, for that reason, the BCJR algorithm is rederived. Simulation results show that woven convolutional codes are attractive alternatives to the celebrated Turbo codes. Finally, a review of bounds, such as error exponents and bounds on the active distances, is given for woven convolutional codes