Abstract
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 detection 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 performvery 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.
Highlights
The discovery of turbo codes and the rediscovery of lowdensity parity-check (LDPC) codes have renewed the research frontier of capacity-achieving codes [1, 2]
We investigate the impact of pilot spacing and filter lengths, and we show that the proposed product accumulate (PA) iterative differential detection and decoding (IDDD) receiver requires very moderate number of pilot symbols, compared to, for example, turbo codes [6]
Through extrinsic information transfer (EXIT) analysis [9], we show that the widespread practice of inserting pilot symbols to periodically terminate the trellis of the differential encoder inevitably [6, 7] incurs a loss in code capacity
Summary
The discovery of turbo codes and the rediscovery of lowdensity parity-check (LDPC) codes have renewed the research frontier of capacity-achieving codes [1, 2] They revolutionized the coding theory by establishing a new softiterative paradigm, where long powerful codes are constructed from short simple codes and decoded through iterative message exchange and successive refinement between component decoders. Viewed from the coding perspective, performing differential encoding is essentially concatenating the original code with an accumulator, or, a recursive convolutional code in the form of 1/(1 + D). In this series of two-part papers, we investigate the theory and practice of LDPC codes with differential encoding. Product accumulate codes, proposed in [4] and depicted in Figure 1, are a class of serially concatenated codes, where the inner code is a differential encoder, and the outer code is a parallel concatenation of two branches of single-parity
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