Minimal Trellises for Linear Block Codes and Their Duals
نویسندگان
چکیده
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity for a fixed permutation of the code. We examine constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code. We identify the primitive structures that can appear in a minimal trellis and relate this to those for the minimal trellis of the dual code.
منابع مشابه
Tail-biting Trellises for Linear Codes and their Duals
Trellis representations of linear block codes are attractive because of their use in soft decision decoding algorithms. An interesting property that is known for conventional trellises is that the minimal conventional trellis (known to be unique) for a linear block code, and its dual have the same state-complexity profile. This interesting property follows from the BCJR construction [1] of the ...
متن کاملTrellis Representations for Linear Block Codes
Trellis Representations for Linear Block Codes Heide Gluesing-Luerssen University of Kentucky Department of Mathematics 715 Patterson Office Tower Lexington, KY 40506 USA During the last decade conventional and tail-biting trellis representations of linear block codes have gained a great deal of attention. A tail-biting trellis for a block code of length n is an edge-labeled layered graph on th...
متن کاملOn the Trellis Structure of Block Codes - Information Theory, IEEE Transactions on
Abst+act-The problem of minimizing the vertex count at a given time index in the trellis for a general (nonlinear) code is shown to be NP-complete. Examples are provided that show that 1) the minimal trellis for a nonlinear code may not be observable, i.e., some codewords may be represented by more than one path through the trellis and 2) minimizing the vertex count at one time index may be inc...
متن کاملOn the Algebraic Structure of Linear Trellises
Trellises are crucial graphical representations of codes. While conventional trellises are well understood, the general theory of (tail-biting) trellises is still under development. Iterative decoding concretely motivates such theory. In this paper we first develop a new algebraic framework for a systematic analysis of linear trellises which enables us to address open foundational questions. In...
متن کاملOn the Intractability of Permuting a Block Code to Minimize Trellis Complexity [Correspondence] - Information Theory, IEEE Transactions on
A novel trellis design technique for both block and convolutional codes based on the Shannon product of component block codes is introduced. Using the proposed technique, structured trellises for block and convolutional codes have been designed. It is shown that the designed trellises are minimal and allow reduced complexity Viterbi decoding. Zndex Terms-Linear codes, trellis structure, product...
متن کامل