A Geometric Description of the Iterative Least-Squares Decoding of Analog Block Codes

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This paper outlines that when decoding an arbitrary analog block codes, i.e., a block codes over the complex or real numbers, in an iterative fashion by splitting the H-Matrix in two, leads to a least-squares estimate. Such a Turbo-like algorithm represents iterative projections in Euclidean space. A step size controls the convergence speed. The paper generalized an earlier result based on array codes (product codes) with analog parity-check component codes. The results in here are considered to be an important step towards an intuitive understanding of iterative decoding schemes of conventional Turbo and LDPC codes.