Part I of a two-part series investigates product accumulate codes, a special class of differentially-encoded low density parity check (DE-LDPC) codes with high performance and low complexity, on flat Rayleigh fading channels. In the coherent detection case, Divsalar's simple bounds and iterative thresholds using density evolution are computed to quantify the code performance at finite and infinite lengths, respectively. In the noncoherent detection case, a simple iterative differential

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... and decoding (IDDD) receiver is proposed and shown to be robust for different Doppler shifts. Extrinsic information transfer (EXIT) charts reveal that, with pilot symbol assisted differential detection, the widespread practice of inserting pilot symbols to terminate the trellis actually incurs a loss in capacity, and a more efficient way is to separate pilots from the trellis. Through analysis and simulations, it is shown that PA codes perform very well with both coherent and noncoherent detections. The more general case of DE-LDPC codes, where the LDPC part may take arbitrary degree profiles, is studied in Part II Li 2008.