Multilevel codes for PSK signaling over the Rayleigh fading channel

Abstract

In this research we investigate the application of multilevel codes to the Rayleigh fading channel, the modulation form at being the MPSK constellation. The first part of the study reveals that effectively twice the diversity is available using multilevel codes than using a simple binary to M-ary mapping. We note that the complexity of decoding the multilevel code is nearly identical to that of decoding the binary mapped code. The second phase of the dissertation focuses on concatenated codes. Of the five systems proposed, one achieves a ninth order diversity for a 4-PSK signal set while another one yields an asymptotic sixteenth order for the 8-PSK constellation. The decoding complexity of the ninth order system can be greatly reduced if staged decoding is used on the inner multi level code. Likewise, the sixteenth order system can be easily implemented using our own soft decoder for the inner even-parity subcodes. We also consider the performance of multilevel structures on a time-varying channel. A practical example is proposed for the radio mobile channel featuring data transmission from a broadcasting station to a moving vehicle. Three dB gain is achieved and a diversity of second order protects the information in the event of a fading. This system has a low complexity level, with a rate 1/2 4-state convolutional code at the first decoding level and a simple rate 1/2 zero-sum code at the second level. Optimal and suboptimal strategies are used to decode the multilevel codes. Hard decisions, soft decisions, and hybrid decoders are also investigated.