In this paper, we derive an asymptotic analysis and optimization of coded CPM systems using both unstructured and protograph-based LDPC codes ensembles. First, we present a simple yet effective approach to design unstructured LDPC codes : by inserting partial interleavers between LDPC and CPM, and allowing degree-1 and degree-2 variable nodes in a controlled pattern, we show that designed codes perform that can operate very close to the maximum achievable rates. Finally, the extension to protograph based codes is discussed. We provide some simple rules to design good protograph codes with good threshold properties.
In this paper, we provide a general framework for spatially-coupled concatenated systems. We explicit the analogy with spatially-coupled protographs and provide an adapted EXIT chart analysis. By proposing a continuousvalued coupling matrix, we propose a code design procedure for faster convergence. When considering general bitinterleaved coded-modulation scheme, we also conjecture that the spatially-coupled scheme of general detectors saturates to a value very close (lower bound) to the threshold given by the Area theorem.
The spatial coupling is an efficient technique that improves the threshold of Low Density Parity Check (LDPC) codes. In this paper, we investigate the performance of the serial concatenation of Continuous phase modulation (CPM) and LDPC convolutional codes over a memoryless additive white Gaussian noise channel. We show that coupling protographs optimized for CPM improves their performance and helps designing very good 'small' protographs. Inspired from convolutional codes and thanks to the inner structure of CPM, we also introduce a new termination without rate loss but that still exhibits a coupling gain and it thus has a very good threshold. We will illustrate the behavior of different LDPC convolutional codes with different termination methods by giving some examples and studying their performance using multidimensional EXIT analysis.
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