Tail-Biting Trellises of Block Codes: Trellis Complexity and Viterbi Decoding Complexity
Summary :
Tail-biting trellises of linear and nonlinear block codes are addressed. We refine the information-theoretic approach of a previous work on conventional trellis representation, and show that the same ideas carry over to tail-biting trellises. We present lower bounds on the state and branch complexity profiles of these representations. These bounds are expressed in terms of mutual information between different portions of the code, and they introduce the notions of superstates and superbranches. For linear block codes, our bounds imply that the total number of superstates, and respectively superbranches, of a tail-biting trellis of the code cannot be smaller than the total number of states, and respectively branches, of the corresponding minimal conventional trellis, though the total number of states and branches of a tail-biting trellis is usually smaller than that of the conventional trellis. We also develop some improved lower bounds on the state complexity of a tail-biting trellis for two classes of codes: the first-order Reed-Muller codes and cyclic codes. We show that the superstates and superbranches determine the Viterbi decoding complexity of a tail-biting trellis. Thus, the computational complexity of the maximum-likelihood decoding of linear block codes on a tail-biting trellis, using the Viterbi algorithm, is not smaller than that of the conventional trellis of the code. However, tail-biting trellises are beneficial for suboptimal and iterative decoding techniques.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.10 pp.2043-2051
- Publication Date
- 1999/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Ilan REUVEN, Yair BE'ERY, "Tail-Biting Trellises of Block Codes: Trellis Complexity and Viterbi Decoding Complexity" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 10, pp. 2043-2051, October 1999, doi: .
Abstract: Tail-biting trellises of linear and nonlinear block codes are addressed. We refine the information-theoretic approach of a previous work on conventional trellis representation, and show that the same ideas carry over to tail-biting trellises. We present lower bounds on the state and branch complexity profiles of these representations. These bounds are expressed in terms of mutual information between different portions of the code, and they introduce the notions of superstates and superbranches. For linear block codes, our bounds imply that the total number of superstates, and respectively superbranches, of a tail-biting trellis of the code cannot be smaller than the total number of states, and respectively branches, of the corresponding minimal conventional trellis, though the total number of states and branches of a tail-biting trellis is usually smaller than that of the conventional trellis. We also develop some improved lower bounds on the state complexity of a tail-biting trellis for two classes of codes: the first-order Reed-Muller codes and cyclic codes. We show that the superstates and superbranches determine the Viterbi decoding complexity of a tail-biting trellis. Thus, the computational complexity of the maximum-likelihood decoding of linear block codes on a tail-biting trellis, using the Viterbi algorithm, is not smaller than that of the conventional trellis of the code. However, tail-biting trellises are beneficial for suboptimal and iterative decoding techniques.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_10_2043/_p
Copy
@ARTICLE{e82-a_10_2043,
author={Ilan REUVEN, Yair BE'ERY, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Tail-Biting Trellises of Block Codes: Trellis Complexity and Viterbi Decoding Complexity},
year={1999},
volume={E82-A},
number={10},
pages={2043-2051},
abstract={Tail-biting trellises of linear and nonlinear block codes are addressed. We refine the information-theoretic approach of a previous work on conventional trellis representation, and show that the same ideas carry over to tail-biting trellises. We present lower bounds on the state and branch complexity profiles of these representations. These bounds are expressed in terms of mutual information between different portions of the code, and they introduce the notions of superstates and superbranches. For linear block codes, our bounds imply that the total number of superstates, and respectively superbranches, of a tail-biting trellis of the code cannot be smaller than the total number of states, and respectively branches, of the corresponding minimal conventional trellis, though the total number of states and branches of a tail-biting trellis is usually smaller than that of the conventional trellis. We also develop some improved lower bounds on the state complexity of a tail-biting trellis for two classes of codes: the first-order Reed-Muller codes and cyclic codes. We show that the superstates and superbranches determine the Viterbi decoding complexity of a tail-biting trellis. Thus, the computational complexity of the maximum-likelihood decoding of linear block codes on a tail-biting trellis, using the Viterbi algorithm, is not smaller than that of the conventional trellis of the code. However, tail-biting trellises are beneficial for suboptimal and iterative decoding techniques.},
keywords={},
doi={},
ISSN={},
month={October},}
Copy
TY - JOUR
TI - Tail-Biting Trellises of Block Codes: Trellis Complexity and Viterbi Decoding Complexity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2043
EP - 2051
AU - Ilan REUVEN
AU - Yair BE'ERY
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1999
AB - Tail-biting trellises of linear and nonlinear block codes are addressed. We refine the information-theoretic approach of a previous work on conventional trellis representation, and show that the same ideas carry over to tail-biting trellises. We present lower bounds on the state and branch complexity profiles of these representations. These bounds are expressed in terms of mutual information between different portions of the code, and they introduce the notions of superstates and superbranches. For linear block codes, our bounds imply that the total number of superstates, and respectively superbranches, of a tail-biting trellis of the code cannot be smaller than the total number of states, and respectively branches, of the corresponding minimal conventional trellis, though the total number of states and branches of a tail-biting trellis is usually smaller than that of the conventional trellis. We also develop some improved lower bounds on the state complexity of a tail-biting trellis for two classes of codes: the first-order Reed-Muller codes and cyclic codes. We show that the superstates and superbranches determine the Viterbi decoding complexity of a tail-biting trellis. Thus, the computational complexity of the maximum-likelihood decoding of linear block codes on a tail-biting trellis, using the Viterbi algorithm, is not smaller than that of the conventional trellis of the code. However, tail-biting trellises are beneficial for suboptimal and iterative decoding techniques.
ER -
English
