Low-Complexity Signal Processing for ISI Channels Stefan Schmermbeck ∗ , Guido Stromberg † , Martin Hassner ‡ , Uwe Schwiegelshohn ∗ ∗ Computer Engineering Institute, University of Dortmund 44221 Dortmund, Germany email: {stefan.schmermbeck, uwe.schwiegelshohn}@udo.edu † Infineon Technologies 81730 Munich, Germany email: stromberg@ieee.org ‡ Hitachi Global Storage Technology HGST San Jose Research Center, Almaden, USA email: martin.hassner@hgst.com Abstract—In this paper, we present a low-complexity soft detection and soft decoding magnetic disk drive read channel with a modified soft output signal space detector (S 3 D) which uses 3D-110 equalization and an error/erasure decoding Reed Solomon (RS) code. The detector determines Max-Log reliability information for intersymbol interference (ISI) channels with stationary white and colored noise. It can be implemented with only little additional hardware compared to the ordinary signal space detector. The erasures of the RS code are determined by the soft information and by an additional inner error detecting code (EDC) which is matched to the error patterns of the S 3 D. The proposed system permits an improvement of the decoding performance in practical hard disk applications. I. I NTRODUCTION Due to the increasing use of hard disks in mobile devices, power consumption and hardware complexity become more important. Nevertheless, the requirements for data integrity are the same as for desktop models. Thus, read channels, which exhibit a good performance at reasonable hardware costs, must be developed. High data integrity can be obtained with soft decoding algorithms, like turbo-codes [1] and low density parity check (LDPC) codes [2], if they are combined with a suitable soft output detection technique. Different soft output detectors have already been proposed for decision feedback equalization (DFE) detectors [3], for partial response maximum likelihood (PRML) channels [4] and for signal space detectors (SSD) [5], [6]. A detector for mobile applications, that calculates reliability information, must exhibit a good performance and implement methods for the determination of the soft outputs with only modest hardware modifications. SSDs [7], [8] are especially suitable for the described pur- pose due to their excellent performance which can be obtained with low hardware complexity [9]. Further, soft output SSDs have already been intensively studied for the digital versatile disk (DVD) optical channel [5] and the magnetic recording channel [6]. The high quality of service, which is required in hard disk environments, demands the use of a powerful error correcting code (ECC). The matter of choice are Reed Solomon (RS) codes which exhibit a good performance at high coderates. They can be used for a fast on-the-fly error correction [10]. Further, Reed Solomon codes can be easily modified to perform error-/erasure decoding [10] which can enhance the performance significantly. Hence, the interaction between a soft output signal space detector and an error/erasure correct- ing Reed Solomon code is an important issue of this paper. To this end, a novel soft output SSD (S 3 D) is presented. The major design constraint is low hardware complexity, which distinguishes our S 3 D from existing soft output SSDs [6]. In addition, the proposed detector considers the influence of error propagation and of colored additive Gaussian noise which occur frequently in hard disk applications since SSDs are usually preceded by forward equalizers. The S 3 D is combined with an error/erasure correcting Reed Solomon code. To this end, the soft outputs of the detector are used to identify unreliable codesymbols while an additional inner error detecting parity check code (EDC) allows the actual detection of an error. Both results are used to determine the erasure positions which are then corrected by the RS code. This way, RS codes can easily be modified to perform soft- decoding. The system is optimized by matching the EDC to the error patterns of the S 3 D. Its excellent performance is demonstrated by presenting simulation results in comparison to various soft output PRML detectors. II. SOFT OUTPUT SIGNAL SPACE DETECTION SSDs use a fixed-delay detection scheme where a vector r is built from the received samples and is then mapped into an (M + 1)-dimensional signal space S . This signal space is partitioned by hyperplanes E j into decision regions R c which correspond to the detector output bits c i . In white noise, the hyperplanes are determined by the perpendicular bisectors of the noiseless signal points in the signal space which are called admissible signal points s c =[s i-M ,... ,s i ]. C denotes the set of all binary data sequences of finite length M +1 that are allowed by the modulation code. Thus, the detector output bit c i-M is entirely determined by the M +1 most recent samples r i-M ,... ,r i from which the ISI terms due to previous decisions have been removed. GLOBECOM 2003 - 3990 - 0-7803-7974-8/03/$17.00 © 2003 IEEE