Digital Communications with Emphasis on Data Modems

9FORWARD ERROR CORRECTION CODING WITHOUT BANDWIDTH EXPANSION

9.1 INTRODUCTION

This chapter focuses on two modulation waveforms that provide coding gain without requiring additional bandwidth beyond that of the transmitted information symbol [1]. The two waveforms are M‐ary multi‐h continuous phase modulation (CPM) and multiphase shift keying (MPSK) trellis‐coded modulation (TCM). The MPSK TCM is also examined in terms of multilevel quadrature pulse amplitude modulation (MQPAM) TCM. Because the information or data is contained in the signal phase function, both of these techniques provide constant envelope waveforms: a necessary condition for robust performance when used with hard‐limiting channels. Furthermore, the capability to provide coding gain without bandwidth expansion is paramount when attempting to achieve the highest possible data rate in narrowband channels with low‐power small aperture disadvantaged terminals. The coding gain for these waveforms is provided by the inclusion of redundant phase states that behave much like the redundant parity bits in conventional bandwidth expansion with forward error correction (FEC) coding techniques as discussed in Chapter 8. The multi‐h CPM waveform provides the redundant phase states by judicious variations of the modulation index h, whereas the MPSK‐TCM waveform provides redundant phase states by the using M′ < M phase states for the source information leaving M – M′ redundant phase states to resolve errors.

In Section 9.2 ...