Multidimensional Signal Processing for High Areal Density Heated-Dot Magnetic Recording

Recent magnetic recording technologies have opened the possibility of reaching densities of 10 Tb/in2. A 2-D magnetic recording (TDMR) scheme has pointed out one of the key technologies for increasing areal density. From the viewpoint of signal processing for TDMR, a recording system is desirable or preferable to be capable of allowing to get readback signals from a group of adjacent parallel tracks and detect recorded data written in these tracks simultaneously. This paper proposes a novel signal processing scheme with coding and detection for bit-patterned media recording (BPMR) which is considered to be TDMR using bit-patterned media. Actually, the proposed signal processing scheme for BPMR gets mixed readback signal sequences from the parallel tracks using a single reading head and these readback signal sequences are equalized to a frequency response given by a desired 2-D generalized partial response system. In decoding process, a single maximum likelihood sequence detector is capable of detecting the equalized signal sequence, and it leads to an increase in the effective transfer rate because the recorded data on the parallel tracks are decoded for each time slot.

To increase an areal density (AD) of an ultra-high density bit-patterned magnetic recording (BPMR) system [1], we have proposed track mis-regristration (TMR) correction method combined with the soft information adjustor (SIA) to cope with the effects of TMR and two-dimensional (2D) interference [2]. However, we found that soft information or log-likelihood ratio (LLR) can be improved to earn better bit-error rate (BER) performances. Therefore, we propose to use two deep neural networks (DNNs), e.g., multi-layer perceptron (MLP) [3] and long short-term memory (LSTM) network [4] that are operated together with an early SIA on a two-head/two-track (2H2T) BPMR system as shown in Fig. 1.The user sequences, xl,k ∈ {±1} of the l-th track and k-th bit, are recorded onto the medium. All readback signals are produced using two readers, which are then sent to TMR predictor [2]; meanwhile, they are equalized by the consistent 2D equalizers. Then, the equalized sequences, zl,k, are fed into the 2D detectors to output LLRs. The SIA is used to first improve the reliability of each LLR sequence before passing them to our proposed schemes based on DNNs to decide the estimated recorded bits, x'l,k.. The LLR that is obtained from SIA under various TMR effects is given as an input dataset, while the recorded sequence is fixed as an output dataset of DNNs. All of readback signals that relate to considered datasets are interrupted with several electronic noise levels. Here, we set all input and output datasets as 5,200 files, each file consists of 2×32,768 bits, which are directly mapped to be as a pair of input and output datasets.Fig. 2 shows BER performances between the proposed and conventional SIA systems [2]. It is clear that the proposed systems yield better BER performances over the conventional system at all TMR levels with and without position jitter. At BER = 10-5, the proposed LSTM gains for about 4.0 and 4.4 dBs over the conventional SIA system for both cases at TMR 0%. We found that LSTM network slightly provides better performance.  A 2H2T BPMR channel with the DNNs based soft-information improvement.  BER performances of the conventional SIA [2] and proposed systems.

Many concepts that are used in multi-dimensional signal processing are derived from one-dimensional signal processing. As a consequence, they are only suited to multi-dimensional signals which are intrinsically one-dimensional. We claim that this restriction is due to the restricted algebraic frame used in signal processing, especially to the use of the complex numbers in the frequency domain. We propose a generalization of the two-dimensional Fourier transform which yields a quaternionic signal representation. We call this transform quaternionic Fourier transform (QFT). Based on the QFT, we generalize the conceptions of the analytic signal, Gabor filters, instantaneous and local phase to two dimensions in a novel way which is intrinsically two-dimensional. Experimental results are presented.

One of the major problems in bit-patterned magnetic recording (BPMR) systems is an inter-track interference (ITI) that can significantly degenerate the system performance, especially at high areal densities (ADs). Generally, the BPMR system with staggered islands experiences less ITI effect than that with regular islands. Therefore, we propose an iterative two-head two-track detection method for a staggered BPMR system to further reduce the ITI effect, which employs two read heads to read two adjacent tracks and decodes them simultaneously. To lessen the ITI, the weighted readback signal of one track, serving as an ITI signal, is subtracted from the readback signal of the other track, and vice versa, before passing the refined readback signal to an iterative decoding process. Hence, the decoded data will be utilized to estimate the ITI signal for the next global iteration, $N_{\mathrm{ G}}$ . Supposing that the refined readback signal has only one-side ITI effect. We also present the design of the $2{\times }3$ target and its compatible equalizer that will be employed in the proposed system. Results demonstrate that the proposed system not only is superior to the conventional system but also has low complexity. Specifically, the proposed system can perform close to the conventional system whose readback signal encounters only one-side ITI effect when $N_{\mathrm{ G}} = 2$ , 3 and 5 iterations for $\text {AD} = 2$ , 2.5, and 3 Tb/in2, respectively.

: This is an annual report on research conducted under the auspices of the Joint Services Electronics Program. Specific topics covered are: multidimensional digital signal processing, signal restoration and detection, morphological systems for multidimensional signal processing, multidimensional processing for sensory arrays, multiprocessor systems and tools for digital signal processing, linear and nonlinear image processing, two-dimensional optical storage and processing, semiconductor quantum wave devices, electromagnetic measurements in the time and frequency domains, and automated radiation measurements for near- and far-field transformations.

This work introduces a geometrical interpretation of the Chinese remainder theorem (CRT) which is novel and which can be profitably used in the field of multidimensional signal processing. The practical application of the proposed result in some multidimensional signal processing procedures is demonstrated.

Neural networks are a soft computing technique with wide application in signal processing as well as system and process modeling. In the present study, multilayer perceptron (MLP) neural networks were employed to process multidimensional signals generated in metal machining operations (including three-dimensional cutting force signals and three-dimensional cutting vibration signals) and to establish a model for predicting the machined surface roughness. This paper describes in detail our methods of multidimensional signal processing and modeling with MLP neural networks. The MLP neural network model developed in the present study fills an important research gap by taking into account the critical effect of tool-edge radius in machining. As compared to regression models, the MLP neural network model developed in the present study has significantly higher accuracy in predicting the machined surface roughness.

The escalating demand for high-density storage of hard disk drives has prompted the innovation of advanced technologies to significantly boost an areal density (AD). Among these, three-dimensional magnetic recording systems incorporating double recording layers and bit-patterned magnetic recording (BPMR) have currently emerged as one promising solution. Therefore, this article investigates the integration of double-layer magnetic recording and BPMR technologies which is called double-layer BPMR, aiming for a substantial increase in AD. The primary focus lies on minimizing inter-layer interference and mitigating two-dimensional interferences by optimizing bit-island sizes for both upper and lower layers under the incorporation of staggered-like recording media arrangement and an array of magneto-resistive readers. Moreover, we also employ a rate-5/6 modulation code for compensating these effects. Detailed examinations reveal that our proposed system has a superior bit-error rate performance compared with conventional single-layer BPMR system.

This paper nonce a volitional path to the Reciprocity Attributes of the Multidimensional Complex Fourier Transform (IFT) or the Infiite Fourier Transform (IFT) finis the Multidimensional Infinite Hartley Transform (IHT). The provenances for the reciprocity attributes of multidimensional IFT are conferred out of the reciprocity attributes of the multidimensional IHT, and this is doable mainly due to the mathematical liaison betwixt the IFT and the IHT. Apres the IHT is a real transform, it is viable to deduce the reciprocity attributes for IFT throughout the whilom in multidimensions. It is quotidian run-through in signal processing and communication engineering to chance upon signals having the same fettle in the temporal- and frequency-bailiwicks, such as the Gaussian function. In such paradigms, the reciprocity attributes can be blisteringly wont for working out the onward and rearward transforms of the signals under query. In multidimensional signal processing where the outgo of perpertration is of superemeinent momentousness and the IFT is the exemplar, and where the reciprocity attributes of the IFT are to be wont, it is propounded to execute these reciprocity attributes of the IFT by using the reciprocity attributes of the IHT which have been philosophized in this paper. This props up in the penny-pinching of the utraexpensive reckoning time and disbursement by moiety of one-c as it is a well-established fact that real transforms take less time for execution than those the complex transforms. Thus, the reciprocity attributes unfolded in this paper can be used in digital video processing and in the solutions of differential equations and integral equations.

The intense requirements of high-speed implementations of MultiDimensional (MD) Digital Signal Processing (DSP) systems justify the Application Specific Integrated Circuits (ASIC) designs and/or multiprocessor implementations. MD retiming has been recently proposed to improve the circuitry performance in high-level synthesis of single-rate MD DSP systems. This paper has conducted new theoretical analysis of MD multirate DSP systems modeled in data-flow graphs, and proposes intercalation of MD multirate systems so that unified MD retiming operations can be applied on multidimensional multirate DSP systems. By retiming and intercalation, full intra-iteration parallelism is achieved and functional elements can be executed simultaneously on circuits for the generic class of MD multirate DSP systems.KeywordsMultirate Signal ProcessingMD Data Flow GraphMultidimenional Retiming

In real-time data-intensive multimedia processing applications, data transfer and storage significantly influence, if not dominate, all the major cost parameters of the design space—namely energy consumption, performance, and chip area. This paper presents an electronic design automation (EDA) methodology for the high-level design of hierarchical memory architectures in embedded data-intensive applications, mainly in the area of multidimensional signal processing. Different from the previous works, the problems of data assignment to the memory layers, of mapping the signals into the physical memories, and of banking the on-chip memory are addressed in a consistent way, based on the same formal model. This memory management framework employs techniques specific to the integral polyhedra based dependence analysis. The main design target is the reduction of the static and dynamic energy consumption in the hierarchical memory subsystem.

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a particular linear signal processing application, such as infinite and finite discrete time, or infinite or finite discrete space, or the various forms of multidimensional linear signal processing. As soon as a signal model is chosen, basic ingredients follow, including the associated notions of filtering, spectrum, and Fourier transform. The shift operator is a key concept in the algebraic theory: it is the generator of the algebra of filters A. Once the shift is chosen, a well-defined methodology leads to the associated signal model. Different shifts correspond to infinite and finite time models with associated infinite and finite z-transforms, and to infinite and finite space models with associated infinite and finite C-transforms (that we introduce). In particular, we show that the 16 discrete cosine and sine transforms are Fourier transforms for the finite space models. Other definitions of the shift naturally lead to new signal models and to new transforms as associated Fourier transforms in one and higher dimensions, separable and non-separable. We explain in algebraic terms shift-invariance (the algebra of filters A is commutative), the role of boundary conditions and signal extensions, the connections between linear transforms and linear finite Gauss-Markov fields, and several other concepts and connections.

Many signal processing systems, particularly in the multimedia and telecom domains, are synthesized to execute data-dominated applications. Their behavior is described in a high-level programming language, where the code is typically organized in sequences of loop nests and the main data structures are multidimensional arrays. Since data transfer and storage have a significant impact on both the system performance and the major cost parameters--power consumption and chip area, the designer must spend a significant effort during the system development process on the exploration of the memory subsystem in order to achieve a cost-optimized design. This paper presents a memory allocation methodology for multidimensional signal processing applications, focusing on the problem of efficiently mapping the multidimensional signals from the algorithmic specification into the physical memory. In a first phase, two previous mapping models are implemented within a common theoretical framework, which is advantageous from both the point of view of computational efficiency and the amount of allocated data storage. Different from all the previous mapping models that aim to optimize the memory sharing between the elements of a same array (creating separate windows in the physical memory for distinct arrays), this proposed mapping model exploit--in a second phase--the possibility of memory sharing between the elements of different arrays. As a consequence, this signal assignment approach yields significant savings in the amount of data storage resulted after mapping.

Uniform nested loops are broadly used in scientific and multidimensional digital signal processing applications. Due to the amount of data handled by such applications, on-chip memory is required to improve the data access and overall system performance. In this study a static data scheduling method, carrot-hole data scheduling, is proposed for multidimensional applications, in order to control the data traffic between different levels of memory. Based on this data schedule, optimal partitioning and scheduling are selected. Experiments show that by using this technique, on-chip memory misses are significantly reduced as compared to results obtained from traditional methods. The carrot-hole data scheduling method is proven to obtain smallest on-chip memory misses compared with other linear scheduling and partitioning schemes.

Call for papers: Multidimensional systems and signal processing