Capabilities of Convolutional Codes: Unequal Error Protection and More

University dissertation from Department of Information Technology, Lund Univeristy

Abstract: Many communication systems obtain enhanced performance by using concatenated coding schemes. Turbo codes and woven convolutional codes are two examples of such schemes. The component codes used in these schemes operate at rates close to or even above capacity where the free distance of a code is not relevant anymore and other distance properties have to be taken into account. This thesis consists of an introduction to convolutional coding followed by a collection of six papers. In Paper A, some general relations between error-correcting and the error-detecting capabilities of a linear code are given. Lower bounds on the detecting and correcting capabilities of a convolutional code for sparse sequences of errors and erasures, respectively, are derived and extended to sequences of error bursts and erasure bursts. Paper B deals with aspects of a minimal realization of an encoding matrix in rational canonical form. Based on this realization, a lower bound on the active distances is derived. A new class of maximum slope convolutional codes providing good performance in case of a very noisy channel is introduced. Paper C shows by several illustrative examples that the criterion used for optimization in Paper B, is, unfortunately or perhaps fortunately, not the only parameter that has to be taken into account. In some applications we require that some data is more reliable than other which leads to the concept of unequal error protection (UEP). UEP for convolutional codes is investigated in the Papers D?F. Some new tools for estimating the error-correcting capabilities for a specific input or output of a convolutional encoder, are introduced and studied in Paper D. This concept is further developed and applied to woven convolutional schemes in Paper E. Finally, simulation results in Paper F demonstrate that a communication system constructed according to these ideas indeed provides good unequal error-correcting performance for information symbols even if non-optimum encoders are used and iterative decoding is applied.