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This document discusses low-density convolutional (LDC) codes, including turbo-codes. It presents a formal theory and construction methods for LDC codes. The principles of iterative decoding for LDC codes are formulated. An iterative decoding algorithm for homogeneous LDC codes is described. In the following two papers, the authors intend to perform a statistical analysis of LDC codes and a theoretical analysis of iterative decoding. Simulation results for decoding homogeneous LDC codes are also presented.

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