New Angles on the Multi-Dimensional Intersymbol Interference Problem

传统的单磁道和光盘存储技术已经达到了它们的密度极限。为了延续存储密度呈指数级增长的历史趋势，业界正在开发二维（2D）存储技术，其中在二维块中写入和/或读取比特。由于读/写系统的低通特性，这些二维存储系统遭受二维符号间干扰（ISI）。2D- isi可以建模为输入块与有限范围2D模糊函数或“掩模”的二维卷积，然后是加性噪声。著名的Viterbi算法（VA）为一维ISI信道上的一维序列检测提供了最大似然序列估计（MLSE）。两个（或更高）维度的问题要困难得多，部分原因是与一维相比，二维缺乏自然秩序。相对而言，二维问题还没有被很好地理解，已知方法的性能也不太令人满意。在最近的出版物中，我们描述了二维ISI均衡算法，该算法基于对损坏的二维数据的锯齿形扫描，其性能大大优于之前发表的所有工作，并且非常接近2D- mlse边界，在给定信噪比（SNR）的最小误码率方面，理论上可实现的最佳性能。此外，我们已经证明，2D均衡器可以利用许多数据文件中存在的2D相关性来实现进一步的性能提升。为了在这些有希望的初步结果的基础上，我们建议开发一个理论框架，用于有效设计和优化二维和高维ISI均衡算法，用于独立和相关数据，包括二进制和非二进制（“M-ary”）符号。本研究采用一种统一的方法对独立和相关的二维数据和多维数据进行多维均值分析；通过设计、分析和演示基于turbo原理的迭代算法来解决问题，turbo原理是一种借鉴于迭代turbo解码算法的概念，该算法已经彻底改变了信道编码领域。pi有一些有希望的初步结果，这些结果有助于指出其他有希望的调查领域；一种迭代行列软决策反馈算法用于二维二进制数据的2D- isi减少，在高信噪比下，该算法比先前发表的最佳结果高出约0.4 dB。一种锯齿形二维ISI均衡算法，当与行-列算法相连接时，在高信噪比下，其性能优于先前发表的最佳结果约0.7 dB，并且在2D MLSE性能范围内达到0.2 dB。一种联合马尔可夫随机场估计和二维ISI均衡的算法，当原始二维二进制源相关时，该算法比单独进行二维ISI均衡可获得高达2 dB的信噪比增益。所提出的迭代算法同时使用行列和锯齿形最大后验（MAP）检测器，它们交换软估计，与先前提出的行列迭代算法相比，显著提高了数据估计。对于二维和三维ISI，以及相关和非相关源数据，将探讨在迭代算法中添加额外扫描阶数的好处。迭代检测将与低密度奇偶校验（LDPC）码的迭代解码相结合，在二维和三维ISI中进行联合解码和检测。将研究新的复杂性降低技术，以处理具有M-ary符号的源的多维ISI。提议的更广泛影响：提议的项目解决了多维ISI中的解码和检测问题。因此，它结合了项目合作伙伴的两个相关但不同的专业领域的技术：图像处理（Sivakumar）和通信（Belzer）。这在两个领域之间的问题公式和已知解决方案技术之间产生了良好的协同作用。提出的研究将为多维ISI均衡问题的ML解决方案提供一类迭代算法，从而显着提高磁和光存储的存储密度和数据速率。该项目还将有利于新兴的全息存储技术，其中激光用于将比特存储在2D页面堆栈中，从而导致页面内2D ISI，并且在更高密度下，由于页面间干扰而导致3D ISI。该项目将在2D和3D存储通道的错误控制编码方面取得进展，从而进一步提高存储密度。最后，我们期望我们提出的用于m - i多维ISI信道的新型复杂性降低技术也将用于在各种电信应用中出现的一维ISI信道。该项目的教育影响将是招收和培养本科生和研究生。该项目每年将资助两名全日制研究生和大约两名本科生，为期三年。此外，在这个项目中创造的新知识将被整合到pi的研究生课程中，包括估计理论、信道编码和数字通信。

Traditional single-track magnetic and optical disk storage technologies have reached their density limits. To continue the historical trend of exponentially increasing storage density, two-dimensional (2D) storage techniques, wherein bits are written and/or read in 2D blocks, are being developed by industry. These 2D storage systems suffer from 2D intersymbol interference (ISI) due to the low-pass nature of the read/write system. The 2D-ISI can be modeled as two-dimensional convolution of the input block with a finite-extent 2D blurring function, or "mask", followed by additive noise.The well-known Viterbi algorithm (VA) provides the maximum likelihood sequence estimate (MLSE) for detection of 1D sequences on 1D ISI channels. The problem in two (or higher) dimensions is considerably more difficult, due in part to the lack of a natural order in 2D as opposed to 1D. Relatively speaking, the 2D problem is not as well understood, and the performance of known methods is less than satisfactory. In recent publications, we describe 2D ISI equalization algorithms, based on zig-zag scanning of the corrupted 2D data, that substantially outperform all previously published work, and that come very close to the 2D-MLSE bound, the theoretically best attainable performance in terms of minimal bit error rate for a given signal-to-noise (SNR) ratio. Also, we have demonstrated that the 2D correlation present in manydata files can be exploited by the 2D equalizer to achieve even further performance gains. To build on these promising preliminary results, we propose to develop a theoretical framework for efficient design and optimization of two and higher-dimensional ISI equalization algorithms, for both independent and correlated data, with both binary and non-binary ("M-ary") symbols.The proposed research employs a unified approach to MLSE for independent and correlated binary and M-ary multi-dimensional data; problems are addressed by designing, analyzing and demonstrating iterative algorithms based on the turbo principle, a concept borrowed from the iterative turbo decoding algorithm that has revolutionized the field of channel coding. The PIs have a number of promising preliminary results that serve to point out additional promising areas of investigation; these preliminary results include:An iterative row-column soft-decision feedback algorithm for 2D-ISI reduction in 2D binary data,which outperforms the best previously published result by about 0.4 dB at high SNR.A zig-zag 2D ISI equalization algorithm, which, when concatenated with the row-column algorithm, outperforms the best previously published result by about 0.7 dB at high SNR, and comes within 0.2 dB of the 2D MLSE performance bound.An algorithm for joint Markov random field estimation and 2D ISI equalization, which achieves up to 2 dB SNR gains over 2D ISI equalization alone, when the original 2D binary source is correlated.The proposed iterative algorithms use both row-column and zig-zag maximum-a-posteriori (MAP) detectors which exchange soft estimates, resulting in significantly improved data estimates compared to previously proposed row-column iterative algorithms. The benefits of adding additional scan orders to the iterative algorithm will be explored, for both 2D and 3D ISI, and for both correlated and non-correlated source data. Iterative detection will be combined with iterative decoding of low-density parity-check (LDPC) codes to perform joint decoding and detection in 2D and 3D ISI. New complexity reduction techniques will be investigatedto handle multi-dimensional ISI for sources with M-ary symbols.Broader impacts of the proposal:The proposed project addresses the problem of decoding and detection in multi-dimensional ISI. As such, it combines techniques from the two related yet distinct fields of expertise of the project's co-PIs: image processing (Sivakumar) and communications (Belzer). This yields a good synergy between problem formulations and known solution techniques between the two fields.The proposed research will produce a class of iterative algorithms for ML solutions to the multidimensional ISI equalization problem, thereby significantly improving storage densities and data rates for magnetic and optical storage. The project will also benefit the emerging technology of holographic storage, wherein lasers are used to store bits in stacks of 2D pages, leading to intra-page 2D ISI, and, at higher densities, 3D ISI due to inter-page interference. The project will result in advances in error control coding for 2D and 3D storage channels, thereby enabling further increases in storage density. Finally, we expect that the novel complexity reduction techniques we propose to develop for M-ary multi-dimensional ISI channels will also be of use on 1D ISI channels, which occur in a wide variety of telecommunication applications.The educational impact of this project will be the recruitment and training of undergraduate and graduate students. The project will support two full-time graduate students and about two undergraduate students per year, for three years. In addition, new knowledge created during this project will be integrated into the PIs' graduate courses in Estimation Theory, Channel Coding and Digital Communications.