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LDPC codes are analyzed and optimized for a non-coherent block fading channel in which there is correlation between the blocks. This extends related work in the literature which considered independent blocks. Low-complexity estimation and estimation-decoding algorithms based on Kalman smoothing are developed, and density evolution is used to analyze and optimize the resulting code. Results indicate that significant gains can be realized by taking inter-block correlation into account, compared to architectures in which the blocks are assumed to be independent. [ABSTRACT FROM AUTHOR]