4.2 Nonrecursive Structure for Tomlinson-hara- Shima Precoding

Figure 12. Nonrecursive structure of Tomlinson–Harashima pre-coding for DC-free channels. to the ideal structure is negligible. In spite of the recur-sive structure, in each case, the precoder remains stable. The overflow handling of two's complement representation results in the desired periodical extension of the signal set at the decoder input. The additional noise at the decision point due to data quantization (preferably by trun-cation) usually can be neglected compared to the channel impairments. The analysis shows the important result, that the order of the whitening filter should not be chosen as high as possible, but there always exists an optimum (often small) order. The proposed alternative, non-recursive structure can be implemented without any quan-tization noise. Additionally, already with small orders of an all-pole whitening filter a high prediction gain can be achieved. Thus, only a few additions and multiplications – but with somewhat higher word-length – are required. Especially if a dynamics restriction is applied, this alternative structure is the first choice. To summarize, using appropriate fixed-point arithmetics Tomlinson–Harashima precoding can be implemented at very little expense in application specific integrated circuits. References [1] Forney, G. D.: Maximum likelihood sequence estimation of digital sequences in the presence of intersymbol interference. Dynamics limited pre-coding, shaping, and blind equalization for fast digital transmission over twisted pair lines.: Design and performance of an all-digital adaptive 2.048 Mbit/s data transmission system using noise prediction. was born in Ans-bach, Germany, in 1966. He received the Dipl.-Ing. degree in electrical engineering from the University of Erlangen-Nürnberg in 1992. Since then, he has been a Research Assistant at the Lehrstuhl für Nachricht-entechnik at the University of Erlangen-Nürnberg, from which he received the Dr.-Ing. degree with a thesis on multi-channel and multi-carrier modulation in 1996. His work concentrates on fast digital transmission over twisted pair lines. Within the framework of research projects with the Deutsche Telekom AG he worked on coordinated transmission for dual-duplex HDSL systems and multi-carrier modulation. His current interests are information theory, digital communications and signal processing, and especially precoding and shaping techniques for high rate transmission schemes. His research interests are information and coding theory, modulation schemes, high rate baseband transmission and algorithms for signal detection and adaptive equalization for channels with severe intersymbol interference. He is author of the book " Trelliscodierung " (Trellis Coding). Figure 10. Prediction gain over the order p of the whitening filter. Figure 11. Nonrecursive structure for Tomlinson–Harashima …