Some Problems in Coding, Coded Modulation, Suboptimum Decoding and Trellis Structure

随着对数据完整性需求的增加， 控制在数据通信中变得越来越重要。 它有 成为几乎所有通信系统设计中不可或缺的一部分。 今天，非常复杂的编码被用于广泛的数据 通信系统。 这个研究项目是一个调查， 编码和编码调制中的一些问题， 在理论和实践上都很重要。 该研究包括四个 相关领域：（1）多级调制码和多级 解码;（2）多级级联编码调制方案， 多维调制码的构造;（3）网格 线性分组码的结构;（4）分组的次优译码 在第一个领域，研究寻求具体的多层次 构造带宽有效的多级调制码的方法 具有良好的最小平方欧几里德距离，小的路径多重性， 以及期望的结构，诸如线性、相位对称和简单的 格子图为了减少路径多样性，适当 信号标记的连续水平之间的相互依赖性 寻找点和组件代码。 此外，还研究了各种多- 多级调制码的分级译码方案。 重点 是设计实现良好误差的多级解码方案 性能和大的编码增益，同时降低了解码复杂度。 在 第二个研究领域是多级连接 研究了采用编码调制技术对数据进行差错控制的方法 通信，以实现高纠错性能，大 编码增益和高频谱效率，减少解码 复杂性 这种多级级联编码调制方案 用于构建长的强大的多维（块或网格） 具有良好相位对称性的调制码。 在第三个研究领域， 重点研究了线性块的网格结构的复杂性 代码. 将使用分组码的布尔多项式表示 来构造它们的最小网格图。 旨在 为了找到代码的比特位置上的特定排列， 降低代码网格的状态复杂度。 重点放在 寻找具有简单网格结构的好代码， 似然解码可以用维特比算法来实现。 的 第四部分是次优软判决译码的研究 对于分组码，其可以被分解成具有 更小的尺寸和更简单的（网格）结构。 其旨在 找到好的代码（如BCH码），这些代码是可分解的，或者是 可分解码的并集

As the demand for data integrity increases, coding for error control becomes increasingly important in data communications. It has become an integral part in almost every communication system design. Today very sophisticated coding is used in a broad range of data communication systems. this research project is an investigation of some problems in coding and coded modulation which are both theoretically and practically important. The research includes four inter- related areas: (1) multi-level modulation codes and multi-stage decoding; (2) multi-level concatenated coded modulation schemes and construction of multi- dimensional modulation codes; (3) trellis structure of linear block codes; and (4) suboptimum decoding of block codes.In the first area, the research seeks specific multi-level methods to construct bandwidth efficient multi-level modulation codes with good minimum squared Euclidean distance, small path multiplicity, and desirable structure such as linearity, phase symmetry, and simple trellis diagrams. To reduce the path multiplicity, proper interdependence between consecutive levels of labeling for signal points and component codes is sought. Also studied are various multi- stage decoding schemes for the multi-level modulation codes. The focus is to devise multi-stage decoding schemes which achieve good error performance and large coding gain with reduced decoding complexity. In the second area of research, multi-level concatenation in conjunction with coded modulation is studied for error control in data communications to achieve high error-correction performance, large coding gain, and high spectral efficiency with reduced decoding complexity. This multi-level concatenated coded modulation scheme is used to construct long powerful multi-dimensional (block or trellis) modulation codes with good phase symmetry. In the third research area, the focus is on the complexity of the trellis structure of linear block codes. Boolean polynomial representation of block codes will be used for the construction of their minimal trellis diagrams. It is intended to find specific permutations on the bit positions of codes which reduce the state complexity of code trellises. Emphasis is placed on finding good codes with simple trellis structure so that maximum likelihood decoding can be achieved with the Viterbi algorithm. The fourth area is an investigation of suboptimum soft-decision decoding for block codes which can be decomposed into constituent codes with smaller dimensions and simpler (trellis) structure. It is intended to find good codes (such as BCH codes) which are decomposable or are unions of decomposable codes.