Analysis of Some Convolutional Coding Constructions

Sammanfattning: This thesis focuses on different convolutional coding constructions for digital communication systems, and on methods to analyze these constructions. The work presented in the thesis can be divided into three main areas; error probability bounds for convolutional codes, analysis of multilevel modulation, and investigation of low-density parity-check convolutional codes. New bounds are developed for the bit and burst error probabilities of convolutional codes that are used for transmission over a binary symmetric channel or an additive white Gaussian noise channel. The new bounds for the burst error probability are significantly tighter than prevalent bounds. Coded modulation is a technique that can be used when constructing bandwidth efficient systems. One form of coded modulation is multilevel modulation, which offers the opportunity to use a suboptimal multistage decoder. This decoder is less complex than the corresponding maximum likelihood decoder is. In this work, multilevel modulation undergoes an asymptotical ensemble analysis in terms of error exponents, and a comparison to the corresponding conventional coded modulation system. Furthermore, the Chernoff bounding parameter is calculated for a number of signal constellations that can be used in multilevel modulation systems. These calculations are done under the assumption that a suboptimal metric, the nearest neighbor metric, is employed in the multistage decoder. For each of these signal constellations, the effective capacity and cutoff rate are also given. Low-density parity-check codes combined with iterative decoding have proved to have the potential to achieve low bit error rates even when operating close to the channel capacity. In this treatise, low-density parity-check convolutional (LDPCC) codes are defined, and different construction methods are presented. A statistical ensemble analysis of LDPCC codes is performed, and it results in bounds on the free distance and on the error probability. Iterative decoding is discussed, an iterative decoding algorithm is given, and simulations are performed for various LDPCC codes.