Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Decoding of codes based on their tailbiting trellises

R.Y. Shao, Shu Wen Lin, M.P.C. Fossorier

Published Nov 7, 2002• 6 citations
Publisher

Abstract

A tailbiting trellis for a code is a trellis with multiple starting and multiple ending states. Each starting state corresponds to a unique ending state and they are the same state. A path in a tailbiting trellis represents a valid codeword if and only if it starts from a state and ends at the same state. Such a path is called a tailbiting path. In this paper, two new iterative algorithms for decoding codes based on their tailbiting trellises are presented, one is unidirectional and the other is bidirectional. Both algorithms are computationally efficient and achieves virtually optimum error performance with a small number of decoding iterations.

DOI
10.1109/isit.2000.866640

Related papers

Error-Trellis Construction for Tailbiting Convolutional Codes

Masato Tajima, Koji Okino

In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the correspondence between code subtrellises in the tailbiting code-trellis and error subtrellises in the tailbiting error-trellis. Also, we present a construction of tailbiting backward error-trellises. Moreover, we obtain the scalar parity-check matrix for a tailbiting convolutional code. The proposed construction is based on the adjoint-obvious realization of a syndrome former and its behavior is fully used in the discussion.

arXiv:1201.4428•IEICE Technical Report; IEICE Tech. Rep.•Jan 21, 2012•3 citations

A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes

Takuya Koumoto, T. Takata, Tadao Kasami +1 more

This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.

IEEE Transactions on Information Theory•Mar 1, 1999•13 citations

An Iterative Soft-Decision Decoding Algorithm

Shu Wen Lin, Takuya Koumoto, Toyoo Takata +1 more

This paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. Simulation results for the RM(64,22), EBCH(64,24), RM(64,42) and EBCH(64,45) codes show that the proposed decoding algorithm achieves practically (or near) optimal error performance with significant reduction in decoding computational complexity. The average number of search iterations is also small even for low signal-to-noise ratio.

•Jul 10, 1996•7 citations

On iterative soft-decision decoding of linear binary block codes and product codes

R. Lucas, Martin Bossert, Markus Breitbach

Iterative decoding methods have gained interest, initiated by the results of the so-called "turbo" codes. The theoretical description of this decoding, however, seems to be difficult. Therefore, we study the iterative decoding of block codes. First, we discuss the iterative decoding algorithms developed by Gallager (1962), Battail et al. (1979), and Hagenauer et al. (1996). Based on their results, we propose a decoding algorithm which only uses parity check vectors of minimum weight. We give the relation of this iterative decoding to one-step majority-logic decoding, and interpret it as gradient optimization. It is shown that the used parity check set defines the region where the iterative decoding decides on a particular codeword. We make plausible that, in almost all cases, the iterative decoding converges to a codeword after some iterations. We derive a computationally efficient implementation using the minimal trellis representing the used parity check set. Simulations illustrate that our algorithm gives results close to soft decision maximum likelihood (SDML) decoding for many code classes like BCH codes. Reed-Muller codes, quadratic residue codes, double circulant codes, and cyclic finite geometry codes. We also present simulation results for product codes and parallel concatenated codes based on block codes.

IEEE Journal on Selected Areas in Communications•Jan 1, 1998•100 citations

Codes and iterative decoding on general graphs

Niclas Wiberg, Hans‐Andrea Loeliger, Ralf Kötter

Abstract A general framework, based on ideas of Tanner, for the description of codes and iterative decoding (“turbo coding”) is developed. Just like trellis‐based code descriptions are naturally matched to Viterbi decoding, code descriptions based on Tanner graphs (which may be viewed as generalized trellises) are naturally matched to iterative decoding. Two basic iterative decoding algorithms (which are versions of the algorithms of Berrou et al. and of Hagenauer, respectively) are shown to be natural generalizations of the forward‐backward algorithm (Bahl et al.) and the Viterbi algorithm, respectively, to arbitrary Tanner graphs. The careful derivation of these algorithms clarifies, in particular, which a priori probabilities are admissible and how they are properly dealt with. For cycle codes (a class of binary linear block codes), a complete characterization is given of the error patterns that are corrected by the generalized Viterbi algorithm after infinitely many iterations.

European Transactions on Telecommunications•Sep 1, 1995•318 citations

Stochastic iterative decoders

Chris Winstead, Vincent Gaudet, Anthony Rapley +1 more

This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the algorithm approaches maximum a-posteriori decoding. We also demonstrate a stochastic approximations to the alternative update rule successive relaxation. Stochastic decoders have very simple digital implementations which have almost no RAM requirements. We present example stochastic decoders for a trellis-based Hamming code, and for a block turbo code constructed from Hamming codes

arXiv:cs/0501090•IEEE International Symposium on Information Theory (ISIT)•Jan 1, 2005•64 citations
A tailbiting trellis for a code is a trellis with multiple starting and multiple ending states. Each starting state corresponds to a unique ending state and they are the same state. A path in a tailbiting trellis represents a valid codeword if and only if it starts from a state and ends at the same state. Such a path is called a tailbiting path. In this paper, two new iterative algorithms for decoding codes based on their tailbiting trellises are presented, one is unidirectional and the other is bidirectional. Both algorithms are computationally efficient and achieves virtually optimum error performance with a small number of decoding iterations.
In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the correspondence between code subtrellises in the tailbiting code-trellis and error subtrellises in the tailbiting error-trellis. Also, we present a construction of tailbiting backward error-trellises. Moreover, we obtain the scalar parity-check matrix for a tailbiting convolutional code. The proposed construction is based on the adjoint-obvious realization of a syndrome former and its behavior is fully used in the discussion.
This paper presents a new low-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The algorithm is devised based on a set of optimality conditions and the generation of a sequence of candidate codewords for an optimality test. The initial candidate codeword is generated by a simple decoding method. The subsequent candidate codewords, if needed, are generated by a chain of low-weight trellis searches, one at a time. Each search is conducted through a low-weight trellis diagram centered around the latest candidate codeword and results in an improvement over the previous candidate codewords that have been already tested. This improvement is then used as the next candidate codeword for a test of optimality. The decoding iteration stops whenever a candidate codeword is found to satisfy a sufficient condition on optimality or the latest low-weight trellis search results in a repetition of a previously generated candidate codeword. A divide-and-conquer technique is also presented for codes that are not spanned by their minimum-weight codewords. The proposed decoding algorithm has been applied to some well-known codes of lengths 48, 64, and 128. Simulation results show that the proposed algorithm achieves either practically optimal error performance for the example codes of length 48 and 64 or near optimal error performance for the (128, 29, 32) RM code with a significant reduction in computational decoding complexity.
Iterative decoding methods have gained interest, initiated by the results of the so-called "turbo" codes. The theoretical description of this decoding, however, seems to be difficult. Therefore, we study the iterative decoding of block codes. First, we discuss the iterative decoding algorithms developed by Gallager (1962), Battail et al. (1979), and Hagenauer et al. (1996). Based on their results, we propose a decoding algorithm which only uses parity check vectors of minimum weight. We give the relation of this iterative decoding to one-step majority-logic decoding, and interpret it as gradient optimization. It is shown that the used parity check set defines the region where the iterative decoding decides on a particular codeword. We make plausible that, in almost all cases, the iterative decoding converges to a codeword after some iterations. We derive a computationally efficient implementation using the minimal trellis representing the used parity check set. Simulations illustrate that our algorithm gives results close to soft decision maximum likelihood (SDML) decoding for many code classes like BCH codes. Reed-Muller codes, quadratic residue codes, double circulant codes, and cyclic finite geometry codes. We also present simulation results for product codes and parallel concatenated codes based on block codes.
Abstract A general framework, based on ideas of Tanner, for the description of codes and iterative decoding (“turbo coding”) is developed. Just like trellis‐based code descriptions are naturally matched to Viterbi decoding, code descriptions based on Tanner graphs (which may be viewed as generalized trellises) are naturally matched to iterative decoding. Two basic iterative decoding algorithms (which are versions of the algorithms of Berrou et al. and of Hagenauer, respectively) are shown to be natural generalizations of the forward‐backward algorithm (Bahl et al.) and the Viterbi algorithm, respectively, to arbitrary Tanner graphs. The careful derivation of these algorithms clarifies, in particular, which a priori probabilities are admissible and how they are properly dealt with. For cycle codes (a class of binary linear block codes), a complete characterization is given of the error patterns that are corrected by the generalized Viterbi algorithm after infinitely many iterations.
This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the algorithm approaches maximum a-posteriori decoding. We also demonstrate a stochastic approximations to the alternative update rule successive relaxation. Stochastic decoders have very simple digital implementations which have almost no RAM requirements. We present example stochastic decoders for a trellis-based Hamming code, and for a block turbo code constructed from Hamming codes