On Analysis and Design of Low Density Generator Matrix Codes for Continuous Phase Modulation

Abstract

We investigate the analysis and design of low density generator matrix (LDGM) codes for continuous phase modulation (CPM). The system uses LDGM codes as an outer code for CPM. For additive white Gaussian noise channels, we derive the union bound to analyze the error floor performance. Design principles for lowering error floors are suggested from this analysis. We propose a design approach of jointly considering the LDGM code degree and the CPM modulation index. Then we consider the rate-adaptive system for slowly fading channels. By changing the rate of the LDGM codes, the information rate of the CPM signals is adapted according to channel variations. We use a low-rate LDGM code as the mother code. Higher rates are achieved by puncturing the output of these codes. To exploit the rate-flexible property of punctured LDGM codes, a rate function is proposed to calculate the rate of each transmitted block. Thus, we can have a quasi-continuous information rate. Numerical results show that this approach can improve the energy efficiency from a discrete-rate adaptation. Using the rate-adaptive approach, up to 11 dB transmitted energy gain can be achieved from the non-adaptive scheme in the low bit-error-rate region (smaller than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ) for minimum shift keying (MSK).