Study of Trellis Coded Modulation and error control coding.

Abstract

In this thesis, we examine some general theoretical features of Trellis Coded Modulation. The codes in use are the recursive Ungerboeck convolutional codes and they are combined with Quadrature Amplitude Modulation over an Additive White Gaussian Noise channel. The search of optimum mappings is first treated and the question of having some smaller punctured constellations from a larger one is considered. Performance evaluation of TCM codes is provided according to geometric conditions that the mappings must stand in order to reduce the complexity of the calculation. Computation of transfer function is provided and this leads to a theoretical analysis for probability expressions of even, symbol and bit errors. A second order term expression is also elaborated which takes into consideration both error events on the trellis and errors on parallel transitions. Computer simulations have been run along with High Density Television transmission parameters. The results are presented and discussed. The use of error control coding techniques makes a great improvement in performance. For this purpose, Reed-Solomon codes have been concatenated with TCM codes, and gone through interleaving to ensure a higher error recovery efficiency.