Iteratively Decodable Convolutional Codes: Analysis and Implementation Aspects

This thesis addresses the theory and implementation aspects of iteratively decodable codes. Iteratively decodable codes include, in particular, Gallager's regular low-density parity-check (LDPC) codes, Tanner's generalized LDPC (GLDPC) codes, turbo codes due to Berrou et. al. and expander codes. In common, these codes have sparse parity-check matrices, a very particular graph representation and they operate effectively near the Shannon capacity limit. The thesis considers two convolutional counterparts of LDPC and GLDPC codes, which we call low-density parity-check convolutional codes and Braided Block Codes. The advantages of these new codes are: i) low encoding complexity, due to their regular structure, ii) good distance properties, the free distance grows linearly with the overall constraint length, iii) low decoding complexity, they are decodable with message passing type algorithms which are parallelizable, iv) they have the potential to achieve a high error correction performance even when they operate close to the channel capacity, v) they reach the iterative decoding limit already at relatively short overall constraint lengths. The definition of these codes is made through their parity-check matrices and/or their graph representations. A theoretical analysis of the properties of the codes is given. Simple code constructions are proposed at the same time as several efficient encoding and decoding algorithm implementations are presented and analyzed