Spectrum-Efficient LDPC Codes for CPM

Low density parity check (LDPC) codes received preliminary study in the early 2000s for use in aeronautical telemetry, which is an application domain that relies exclusively on continuous phase modulation (CPM) waveforms due to their power and spectrum efficiency under severe size, weight, and power (SWAP) constraints. The limited deployment of LDPC in telemetry has proved to be very successful, which has motivated interest in finding an LDPC solution with comprehensive applicability to all CPM waveforms used in the IRIG-106 telemetry standard. Such a solution, however, has proved to be elusive due to the "coded" nature of CPM itself and its nonlinear characteristics. In this paper, we lay out a design methodology that begins with an extrinsic information transfer (EXIT) characterization of CPM. We show how to incorporate these EXIT characteristics into a protomatrix search that optimizes the decoding threshold for a given CPM scheme. From there, we employ protomatrix lifting techniques to arrive at final quasi-cyclic LDPC codes with desired code rates and information block sizes. Our simulation results demonstrate performance around one dB from the respective waveform channel capacities with no error floors observed at error rates below 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−8</sup>. As such, these codes can be considered to fill in the options for LDPC codes that are currently absent in the IRIG-106 standard.