Error control techniques for satellite and space communications

Shannon's capacity bound shows that coding can achieve large reductions in the required signal to noise ratio per information bit (E sub b/N sub 0 where E sub b is the energy per bit and (N sub 0)/2 is the double sided noise density) in comparison to uncoded schemes. For bandwidth efficiencies of 2 bit/sym or greater, these improvements were obtained through the use of Trellis Coded Modulation and Block Coded Modulation. A method of obtaining these high efficiencies using multidimensional Multiple Phase Shift Keying (MPSK) and Quadrature Amplitude Modulation (QAM) signal sets with trellis coding is described. These schemes have advantages in decoding speed, phase transparency, and coding gain in comparison to other trellis coding schemes. Finally, a general parity check equation for rotationally invariant trellis codes is introduced from which non-linear codes for two dimensional MPSK and QAM signal sets are found. These codes are fully transparent to all rotations of the signal set

Multiple trellis coded 16 QAM.

by Kingsley, King-chi, Kwan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 85-88).Tables of ContentsLists of Figures & TablesAcknowledgmentsAbstractChapter Chapter 1 --- IntroductionChapter 1.1 --- Digital Communication System --- p.P. 1Chapter 1.2 --- Channel Coding --- p.P. 1Chapter 1.3 --- Convolution Encoder --- p.P. 4Chapter 1.4 --- Additive White Gaussian Noise (AWGN) Channel --- p.P. 7Chapter 1.5 --- Trellis Diagram --- p.P. 8Chapter 1.6 --- Error Event and Free Distance --- p.P. 8Chapter 1.7 --- Euclidean Distance --- p.P. 10Chapter 1.8 --- Organization of the Thesis --- p.P. 11Chapter Chapter 2 --- QAM and MTCMChapter 2.1 --- Introduction --- p.P. 13Chapter 2.2 --- M-ary Quadrature Amplitude Modulation (QAM)Chapter 2.2.1 --- M-ary Digital Modulation --- p.P. 13Chapter 2.2.2 --- Quadrature Amplitude Modulation (QAM) --- p.P. 14Chapter 2.2.3 --- Probability of Bit Error of M-ary QAM --- p.P. 16Chapter 2.3 --- Trellis Coded Modulation (TCM) --- p.P. 17Chapter 2.4 --- Multiple Trellis Coded Modulation (MTCM) --- p.P. 19Chapter Chapter 3 --- Set Partitioning of Signal SetsChapter 3.1 --- Introduction --- p.P. 21Chapter 3.2 --- Traditional Set Partitioning MethodsChapter 3.2.1 --- Ungerboeck's Set Partitioning Method --- p.P. 21Chapter 3.22 --- Set Partitioning by M.K. Simon and D. Divsalvar --- p.P. 23Chapter 3.3 --- The new Set Partitioning MethodChapter 3.3.1 --- Nomenclature of the Signal Points in the Signal Constellations --- p.P. 24Chapter 3.3.2 --- Generation of the Signal Sets --- p.P. 26Chapter 3.3.3 --- Partitioning of the Signal SetsChapter 3.3.3.1 --- Input Constraints of the Partitioning Method --- p.P. 30Chapter 3.3.3.2 --- The Set Partitioning Method --- p.P. 30Chapter 3.3.4 --- Distance Properties of the Partitioned Signal Sets --- p.P. 36Chapter 3.3.5 --- The Selection Scheme --- p.P. 39Chapter 3.3.6 --- Assignment of Signal Subsets into Trellis --- p.P. 42Chapter Chapter 4 --- Performance EvaluationChapter 4.1 --- Introduction --- p.P. 46Chapter 4.2 --- Upper Bound of Error ProbabilityChapter 4.2.1 --- Probability of Symbol Error --- p.P. 46Chapter 4.2.1.1 --- Upper Bound on Probability of Symbol Error --- p.P. 48Chapter 4.2.1.2 --- Computation of the Transfer Function --- p.P. 49Chapter 4.2.2 --- Probability of Bit Error --- p.P. 51Chapter 4.3 --- Computation of the Free Distance --- p.P. 53Chapter Chapter 5 --- Results Presentation and DiscussionsChapter 5.1 --- Introduction --- p.P. 58Chapter 5.2 --- Results PresentationsChapter 5.2.1 --- Normalized Square Free Euclidean Distance --- p.P. 58Chapter 5.2.2 --- Error Probability --- p.P. 71Chapter 5.3 --- Discussions --- p.P. 77Chapter Chapter 6 --- Conclusions --- p.P. 83Bibliography --- p.P. 85Chapter Appendix A - --- Flowchart of the Program --- p.P. 89Chapter Appendix B - --- Tabulated Results of d2free --- p.P. 10

Error control techniques for satellite and space communications

The results included in the Ph.D. dissertation of Dr. Fu Quan Wang, who was supported by the grant as a Research Assistant from January 1989 through December 1992 are discussed. The sections contain a brief summary of the important aspects of this dissertation, which include: (1) erasurefree sequential decoding of trellis codes; (2) probabilistic construction of trellis codes; (3) construction of robustly good trellis codes; and (4) the separability of shaping and coding