Fixed Delay Tree Search Research Articles

A reduced high dimensional FDTS for magneto-optical recording

FDTS (Fixed Delay Tree Search) sequence detection using metric calculation is demonstrated. FDTS with a long tree depth is performed using a High Dimensional Signal Space Detector. We propose a new HD (High Dimensional)-FDTS employing a reduction algorithm under conditions of a certain minimum RLL (Run Length Limitation) of code and with ISI (intersymbol interference). We made sure that the HD-FDTS minimum distance taking account of the RLL code was close to that of a Viterbi decoder. The decoder circuit is small and high speed and has a reasonable noise margin for an ideal equalized wave with AWGN (Additive White Gaussian Noise). The HD-FDTS may be applied to PLL (Phase Locked Loop) and AGC (Automatic Gain Control) because of the short decoding delay.

Architectures for the implementation of a fixed delay tree search detector

This paper examines the tradeoff between fixed delay tree search (FDTS) detector complexity and performance with various modulation codes. Several architectures suitable for implementing FDTS or achieving performance comparable to FDTS are presented. Recursive forms are derived by decomposing the branch metric computation while breaking down the entire path metric yields nonrecursive forms. The final architecture casts the detection problem into a signal space context in which the observation space is partitioned into decision regions. These structures are presented and evaluated in the context of an analog very large scale integration (VLSI) implementation. Compared to a direct mapping to hardware of the original algorithm, these alternative schemes offer reduced power consumption and/or increased data rate.

Fixed sample rate Bayesian detector in a variable speed magnetic channel

A new design of blind equalizer is proposed that can decode a magnetic binary channel whose bit-rate is unknown. It is shown that the velocity can be estimated from information already known from a fixed delay tree search (FDTS) decision feedback equalizer (DFE) structure. Converting this detector to a Bayesian scheme with an appreciation of non-linear distortion in the read head modestly improves the velocity stability. The acquisition time for the channel speed is linear and rapid: a 50% change in velocity can be accommodated in fewer than 150 magnetic flux transitions. Results with real signals from a high-density magnetic credit card are provided.

A systematic approach to signal space detection

A general procedure is developed to implement the fixed delay tree search (FDTS) detector in the multi-dimensional signal space. The procedure systematically finds a required set of hyperplanes that divide the entire space into different decision regions. A Boolean mapping function is also analytically determined which generates a final binary decision from several intermediate binary variables that indicate the position of the observation vector relative to given hyperplanes. The proposed technique is demonstrated on a (1+D)/sup 2/ partial response channel driven by the (1,k)-coded input.

Design of multilevel decision feedback equalizers

Multilevel decision feedback equalization scheme (MDFE) is an efficient and simple realization of the fixed-delay tree search with decision feedback (FDTS/DF) for channels using RLL(1,k) codes. In MDFE, the entire tree-search is replaced with a 2-tap transversal filter and a binary comparator with negligible loss in performance. This 2-tap filter can be combined with the forward and feedback equalizers resulting in a structure that is physically identical to DFE but requires very different equalizer settings. This paper focuses on equalizer design for MDFE. It is first shown that the MDFE scheme can also be derived without using the principle of tree-search by exploiting the run-length constraints imposed by the RLL(1,k) code in conjunction with the maximization of an appropriately defined signal-to-noise ratio (SNR). Recognizing that a multilevel eye Is formed at the comparator, we define this SNR as the eye-opening divided by noise plus intersymbol interference. This formulation directly leads to a novel adaptive scheme based on the well known LMS algorithm. The relationship between this work and the earlier derivation of MDFE is then clarified. We also develop a noniterative analytical approach for the optimum equalizer design. Because of the economy of implementation, there is particular interest in the design of continuous-time forward equalizers. A noniterative analytic design approach, which does not suffer from local minima problems, is developed for such equalizers. Computer simulation results are presented for comparing the different design approaches.

Maximum transition run codes for data storage systems

A new code is presented which improves the minimum distance properties of sequence detectors operating at high linear densities. This code, which is called the maximum transition run code, eliminates data patterns producing three or more consecutive transitions while imposing the usual k-constraint necessary for timing recovery. The code possesses the similar distance-gaining property of the (1,k) code, but can be implemented with considerably higher rates. Bit error rate simulations on fixed delay tree search with decision feedback and high order partial response maximum likelihood detectors confirm large coding gains over the conventional (0,k) code.

Equalization and detection in storage channels

In this work, a model for digital magnetic recording on thin-film media is developed, and the performances of several detector/run-length-limited code combinations are compared under different densities, media noise, offtrack interference, and channel mismatch conditions. The study is based on computer simulations using an experimentally extracted transition response of a magnetoresistive read head. The detection algorithms considered include the partial response maximum likelihood detectors, decision feedback equalizer (DFE), and fixed-delay tree search with decision feedback (FDTS/DF) detector. It was found that the DFE with a (0,k) run-length-limited (RLL) code and the FDTS/DF with a (1,7) RLL code show the least bit error rate degradation, as the user density increases beyond 2.5 bits/PW50. The PRML and DFE suffer less from offtrack interference. The (0,k) coded DFE and the (1,7) coded EPRML and FDTS/DF channels are relatively robust under PW50 mismatch. At a user density of 2.5, FDTS/DF (1,7) and DFE (0,k) are found to yield the best bit error performance under varying intensities of white Gaussian noise and media noise.

Analog implementation of the FDTS/DF detection algorithm for magnetic recording

An analog implementation of the fixed delay tree search algorithm for magnetic recording detection is presented. The circuit is designed using a 1.2 /spl mu/m BICMOS process with NPN devices with an f/sub t/ of 12 GHz, and provides a reference for the feasibility of an analog implementation. Composite simulation results of all the system blocks suggest operating speeds in excess of 100 MSamples/s with a total power consumption of less than 1 W.

Adaptive continuous-time equalization followed by FDTS/DF sequence detection

Employing an adaptive continuous-time forward equalizer with a Fixed Delay Tree Search with Decision Feedback (FDTS/DF) detector provides several advantages to a magnetic recording system. Although an adaptive continuous-time filter of modest complexity cannot achieve the degree of pulse shape control provided by a long FIR filter, its power consumption may be dramatically lower. An FDTS/DP detector can be easily adapted to widely varying equalized pulses. By combining the two, we can achieve channel performance comparable to that of a system including an FDTS/DF detector and a long FIR equalizer-but with a power dissipation that is potentially much less than conventional sequence detection channels. Simulation results are presented that compare this new approach with a finite length FIR equalizer followed by an FDTS/DP detector. We present and compare several architectures for the adaptive continuous-time equalizer that offer improved convergence when using the least-mean-squares (LMS) adaptation algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multi-level decision feedback equalization: an efficient realization of FDTS/DF

Multi-level decision feedback equalization (MDFE) is a detection technique which achieves equivalent error rate performance to fixed-delay tree search with decision feedback equalization, while using the simpler architecture of decision feedback equalization. The desired equalization target in MDFE is accommodated by a low order IIR filter, thereby suggesting that all of the forward filtering can be done with continuous-time filters. A potentially low power architecture for MDFE will be described which includes circuit considerations for the phase and gain detectors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of TCPR and FDTS/DF for high-density magnetic recording

We compared the performance of trellis-coded partial response (TCPR) and fixed delay tree search with decision feedback (FDTS/DF) in a recording system with both electronic and medium noise characterized by Thurlings' model. To distinguish influences of the noise correlation on the Viterbi algorithm and the tree search algorithm, the bit error rate with and without noise correlation was calculated by using a noise correlation coefficient after equalization. We obtained the signal-to-noise ratio required for a bit-error-rate of 10/sup -9/, versus a normalized recording density for recording system with 50% electronic noise and 50% medium noise. The results indicate that TCPR gives the best performance for low linear recording density.

Adaptive continuous-time equalization and FDTS/DF sequence detection

An adaptive analog continuous-time forward equalizer and a Fixed Delay Tree Search with Decision Feedback (FDTS/DF) detector can be used to implement high speed low power sequence detection for a magnetic recording system. An analog continuous-time forward equalizer offers a low power, high speed solution to the equalization problem, although it cannot achieve the degree of pulse shape control provided by a long FIR filter. However, an FDTS/DF detector can be easily adapted to cope with the resulting imprecisely equalized pulses. Earlier work demonstrated the suitability of a Complex Graphic Equalizer (CGE) for the adaptive continuous time forward equalizer. System simulations indicated the viability of a CGE-FDTS/DF detector in a 2/3(1,7) coded channel. New results explore the performance of a CGE-FDTS/DF system for an 8/9(0,3) coded channel. Additionally, the feasibility of a CGE-EPR4 detection system is demonstrated.

Constrained-complexity equalizer design for fixed delay tree search with decision feedback

Fixed delay tree search with decision feedback (FDTS/DF) is a hybrid detection scheme which incorporates a sequence detector into the decision feedback equalizer (DFE). When applied to minimum-runlength-limited channels, the FDTS/DP provides near-optimal detection performance with a reasonable complexity requirement. It has been shown recently that for the special case of search depth 1 and the channel subject to the d=1 run length constraint, a simpler structure arises for the decision elements of the FDTS/DF, which provides asymptotically-equivalent performance to the originally proposed FDTS/DF structure. We demonstrate the asymptotic optimality of this reduced FDTS/DF based on a simple signal-to-noise ratio argument. We also introduce a design criterion for choosing tap weights for the constrained-complexity FDTS/DF, which assumes the finite impulse response (FIR) structure for its forward and feedback filters. A method to compute optimal tap weights for the forward and feedback filters is then presented for a magnetic recording channel subject to the popular minimum runlength constraint, d=1. Results show that under the d=1 constraint, the FDTS/DF with one-bit decision delay achieves a large performance improvement over the DFE. >

Efficient sequence detection for intersymbol interference channels with run-length constraints

This paper addresses the data detection problem of intersymbol interference (ISI) channels with a specific modulation code-constraint known as the (d, k) run-length-limited (RLL) constraint, a popular modulation code-constraint for data storage channels as well as certain communication channels. A computationally efficient sequence detection algorithm is proposed which yields a performance close to that of the maximum likelihood sequence detector when applied to such ISI channels. The proposed detector is derived as a high signal-to-noise ratio approximation to the delay-constrained optimum detector, one which minimizes the symbol error probability given a fixed decision-delay constraint. The proposed algorithm is essentially a fixed-delay tree search (FDTS) algorithm with systematic ambiguity checking and is closely related to existing finite-depth tree search algorithms. It is observed that long critical error events common in uncoded ISI channels are eliminated by the RLL constraint. Based on this observation, we show that for some important RLL constrained channels, the proposed FDTS algorithm yields the same minimum Euclidean distance between distinguishable channel output sequences as the unconstrained maximum likelihood sequence detector.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multi-level decision feedback equalization for saturation recording

An impediment to the practical use of fixed-delay tree search with decision feedback (FDTS/DF) for retrieving data from hard disk drives is that four additions and one multiplications must be evaluated in one clock cycle. It is shown here that on recording channels using 2/3

Comparison of computationally efficient forms of FDTS/DF against PR4-ML

The authors compare the error-rate performance and circuit complexity of fixed-delay tree search with decision-feedback (FDTS/DF) to that of Class IV partial response equalization followed by Viterbi detection (PR4-ML). The impact of realistic impulse responses, misequalization, phase errors, and offtrack interference on both detection strategies is explored. Two computationally efficient methods for implementing FDTS/DF are presented. These FDTS/DF architectures avoid explicit multiplication-one uses a RAM-based table lookup and the other uses binary equalization over the tree-depth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Signal-to-noise ratio degradation with channel mismatch (in magnetic recording)

Sensitivities of different run-length-limited coding and equalization/detection schemes to channel response variations have been investigated. Channel variations considered are due to the head-medium velocity variations and head-medium spacing fluctuations, reflected in the height and width changes in the read pulse. Given equalizers/detectors are first tuned to a specific value of PW50, the half-height width of the read pulse. The signal-to-noise ratio degradation was observed as the actual PW50 is varied around this nominal value. The results show that the sensitivity varies widely across different detectors. For example, the partial response maximum likelihood (PRML) schemes, which achieve large performance advantages over peak detection under ideal conditions, are highly sensitive to channel variations and perform worse than peak detection as the PW50 mismatch becomes large. On the other hand, the recently introduced fixed-delay tree search with decision feedback (FDTS/DF) exhibits good resistance to channel variations while achieving favorable nominal performance. >

Detection performance in the presence of transition noise

The performance of various detector/RLL (run-length-limited) code combinations was investigated assuming the presence of both additive white noise and transition noise. The results indicate that for detectors relying heavily on linear suppression of ISI (intersymbol interference), the transition-noise effect does not show up at high densities because of relatively severe enhancement of the additive-noise component. However, transition noise degrades performance of FDTS/DF (fixed delay tree search with decision feedback) and DFE (design feedback equalizer), as a large amount of ISI is allowed at the equalizer output to avoid the excessive additive-noise enhancement. Nevertheless, the FDTS/DF still has substantial performance gain over other detectors. Effects of position jitter and width variations have also been observed separately. It was found that the simple peak detector performs comparatively well in the presence of position jitter, whereas sequence detection schemes that permit a relatively large amount of ISI at the linear equalizer output are more sensitive to position jitter than to width variations, except at low uncoded-densities. It was also observed that the signal-to-noise ratio penalty incurred by the d-constraint is significantly reduced in the transition-noise environment compared to the additive-noise environment.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance comparison of detection methods in magnetic recording

Various detection schemes suitable for magnetic recording are compared in terms of their effective signal-to-noise ratios. It is shown that at high densities the performance of conventional detectors such as a peak detector, a threshold detector with partial response equalization, a decision feedback equalizer, and a Viterbi algorithm detector tuned to a linearly truncated channel fall far below the optimum performance that can be achieved by the maximum-likelihood sequence detector (MLSD). It is shown that while implementing the full MLSD is clearly out of the question for high densities with severe intersymbol interference (ISI), there exists an efficient detection scheme which achieves an excellent compromise between hardware complexity and detection performance. This scheme, which is called the fixed-delay tree search with decision feedback, combines a fast and efficient tree-search algorithm with a decision feedback equalizer to cancel out a portion of ISI without noise enhancement. It is well suited for run-length-limited systems and attains performance close to that of MLSD while maintaining reasonable implementation cost and processing requirements. >