Multilevel turbo coded–continuous phase frequency shift keying (MLTC–CPFSK) q Niyazi Odabasioglu, Osman N. Ucan * Istanbul University Engineering Faculty, Electrical and Electronics Engineering Dept. 34320 Avcilar, Istanbul, Turkey article info Article history: Received 9 February 2007 Received in revised form 15 September 2008 Accepted 3 November 2008 Available online 21 December 2008 Keywords: Continuous phase frequency shift keying Multilevel coding Turbo codes abstract In this paper, we introduce a Turbo coded modulation scheme, called multilevel turbo coded–continuous phase frequency shift keying (MLTC–CPFSK). The underlying basis of multilevel coding is to partition a signal set into several levels and to encode separately each level through the respective layer of the encoder. In MLTC–CPFSK, to provide phase continuity of the signals, turbo encoder and continuous phase encoder (CPE) are serially concatenated at the last level, while all other levels consist of only a turbo encoder. There- fore, the proposed system contains multiple turbo encoder/decoder blocks in its architec- ture. The parallel input data sequences are encoded by our multilevel scheme and mapped to CPFSK signals. Then, for the purpose of performance analysis, these modulated signals are passed through AWGN and fading channels. At the receiver side, the input sequence of the first level is estimated by the first turbo decoder block. Subsequently, the other input sequences of other levels are computed using the estimated input bit streams of the respective previous levels. Simulation results are drawn for 4-ary CPFSK two level and 8-ary CPFSK three level turbo codes over AWGN, Rician, and Rayleigh channels for three iterations while frame sizes are chosen as 100 and 1024. It is concluded that satisfactory performance is achieved in MLTC–CPFSK systems for all SNR values in various fading environments. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Turbo codes are error correction codes that were introduced along with a practical decoding algorithm [1]. The impor- tance of Turbo codes is that they enable reliable communications with power efficiencies close to the theoretical limit pre- dicted by Shannon. Turbo codes are the most efficient codes for low-power applications such as deep space and satellite communications, as well as for interference limited applications such as third generation cellular and personal communica- tion services. In trellis based structures, to improve the bit error probability, many scientists not only study the channel parameters as in [2,3] but as in [4–7] they have also used multilevel coding as an important band and power efficient technique, since it provides significant amount of coding gain and low coding complexity. Multilevel encoder is a combination of several error correction codes applied to subsets of some signal constellation. The multilevel coding scheme employs, at each signaling interval one or more output bits of each of several binary error-control encoders to construct the signal to be transmitted. An important parameter of a coded modulation scheme is the computational complexity of the decoder. Usually, a kind of suboptimal decoder, called the multistage decoder, is used for multilevel codes [6–8]. Nowadays, there are also many 0045-7906/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compeleceng.2008.11.007 q This work was supported by Istanbul University Research Fund, Project no: T-580/17032005. * Corresponding author. Tel.: +905326403979; fax: +902124737064. E-mail addresses: niyazio@istanbul.edu.tr (N. Odabasioglu), uosman@istanbul.edu.tr (O.N. Ucan). Computers and Electrical Engineering 35 (2009) 441–449 Contents lists available at ScienceDirect Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng