An error-trellis is a directed graph that represents all the sequences belonging to the coset which contains the symbol-by-symbol detected version of a given received sequence. A modular construction of error-trellises for an (n,k) convolutional code over GF(q) is presented. The trellis is designed on the basis of partitioning the scalar check matrix of the code into submatrices of l rows, accompanied with a corresponding segmentation of the syndrome. The value of the design parameter l is an essentially unconstrained multiple of n-k. For all the cosets of the code, the sections of the error-trellis are drawn from a collection of only q/sup l/ modules; the module for each section is determined by the value of the associated syndrome segment. In case the construction is based on a basic polynomial check matrix, either canonical or noncanonical, then the error-trellis is minimal in the sense that /spl sigma//spl les//spl mu/, where /spl sigma/ is the dimension of the state space of the trellis and /spl mu/ is the constraint length of a canonical generator matrix for the code. For basic check matrices with delay-free columns, the inequality reduces to /spl sigma/=/spl mu/.
展开▼
机译：误差格是一个有向图，表示代表陪集的所有序列，其中包含给定接收序列的逐符号检测版本。提出了GF（q）上（n，k）卷积码的误差网格的模块化构造。网格的设计是基于将代码的标量校验矩阵划分为1行的子矩阵，并伴随着相应的综合症分割。设计参数l的值基本上是n-k的不受约束的倍数。对于所有代码陪集，错误网格的各个部分仅从q / sup l /个模块的集合中得出；每个部分的模块由关联的综合症段的值确定。如果构造基于规范的或非规范的基本多项式校验矩阵，则在/ spl sigma // spl les // spl mu /的意义上，误差网格最小，其中/ spl sigma /是维网格的状态空间和/ spl mu /是代码的规范生成器矩阵的约束长度。对于具有无延迟列的基本检查矩阵，不等式减小为/ spl sigma / = / spl mu /。
展开▼
