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

Asia-Pacific Conference on Communications (APCC)

Bit- and trellis- based soft-decision sequential decoding for variable-length error-correcting codes

 Huang, Lo, Han

Published Jan 1, 2008• 0 citations
OpenAlex

Related papers

Optimal encoding, trellis structure, and normalized weight of linear block codes.

Houshou Chen

This thesis concentrates on studying three problems in error-correcting codes: optimal encoding, trellis structure, and normalized weight of linear block codes. In general, the research in error-correcting codes can be roughly classified into coding practice and coding theory. The problems in coding practice focus on codes and decoders with more attention on the subject of the tradeoffs between performance and complexity, e.g., soft-decision decoding, bit error probability, or trellis of the codes. On the other hand, coding theory concentrates on the structure of codes based on sophisticated mathematical techniques, with little concern for the decoding complexity, e.g., coset weight distribution, algebraic constructions, or bounds on possible parameters of the codes. In this dissertation, we will present three fundamental topics in coding practice: optimal encoding of linear block codes for bit error probability, trellis structure of linear block codes for trellis-based decoding, and normalized weight of block coded modulation for bandwidth efficient communication systems. The central theme of the thesis is to transform the problems of the above three topics in coding practice into problems in coding theory and to develop the theory associated with the problems. Much of this thesis is devoted to studying what 'optimal' means in different contexts. In summary, we investigated the optimal information bit encoding of a given linear block code for minimizing the probability of an information bit error, with the goal of determining an optimal generator matrix by using the structure of the code. We showed that many natural codes have systematic optimal generator matrices in the quiet region. We analyzed the trellis structure of a self-dual code C to minimize the trellis complexity of the code by considering all equivalent codes of C, with the goal of reducing the soft-decision decoding complexity via permutations on the codeword coordinates. We determined the length/dimension profile of all eight [32, 16, 8] self-dual codes, and find their corresponding optimum permutations. We examined the performance gains achievable by adding interblock memory to block coded modulation systems, with the goal of finding the best codes for normalized distance rather than Hamming distance. We found a large number of best codes for normalized distance for the cases of practical interest.

•Jan 1, 1999•3 citations

Sequential Decoding Algorithms for Block Error-Correcting Codes

Yibin Ng, Wai Ho Mow

•Jan 1, 1998•0 citations

Soft-Decision Decoding Algorithms for Binary Linear Block Codes

Hitoshi Tokushige

•Dec 19, 2000•0 citations

On Unequal Error Protection Reed-Muller Codes

Dojun Rheel

It is well known that Reed-Muller (RM) codes are not an linear unequal error protec- tion (LUEP) code because the set of minimum-weight vectors span Reed-Muller codes (punctured or not) (1,2). In this paper, we showed that most of RM codes are LUEP codes if RM codes are encoded with recursively decomposed trellis oriented generator ma- trix (TOGM) and maximum-likelihood trellis decod- ing (MLTD) is used. I. INTRODUCTION Uneqaul error protection codes protect some information bits against a great number of errors than other information bits. LUEP codes were first introduced by Masnick and Wolf (3). Boyarinov and Katsman (4) found conditions for linear codes to be LUEP. Let C be and (n, IC, d) linear code. It is shown in (l) that if the minimum-weight vectors of a linear code C does not span it, then C is an LUEP code. It is well known that their set of minimum-weight vectors span RM codes (punctured or not) (2). Therefore, RM codes are not LUEP codes in algebraic decoding. In the soft-decision maxi- mum likelihood decoding, bit-error-rate of RM code depends on the weight distribution of code. If non-systematic GM is used for encoding the RM code and soft-decision maximum likelohood decoding is used in decoding, different set of in- formation bits has a different bit-error-rate since each other has different weight distribution. Therefore, even though RM code is not an LUEP code in algebraci decoding, RM code is an LUEP code in soft-decision maximum likelihood decoding if systematic GM is not used for encoding. Especially, in this paper, LUEP RM codes are constructed by using recursively decomposed TOGM for encoding. Sim- ulations show that bit-error-rate of some information bits is almost twice better than that of the other information bits. By using the recursive decomposition, a simple trellis diagram with parallel structure for the RM code is devised. In ML trellis decoding, information bits are retrieved directly from the labeling of the trellis.

•Jan 1, 2000•0 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

Soft-Decision Decoding Algorithm for Binary Linear Block Codes

Yong-Geol Shim, Choong Woong Lee

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Nov 25, 1993•0 citations
This thesis concentrates on studying three problems in error-correcting codes: optimal encoding, trellis structure, and normalized weight of linear block codes. In general, the research in error-correcting codes can be roughly classified into coding practice and coding theory. The problems in coding practice focus on codes and decoders with more attention on the subject of the tradeoffs between performance and complexity, e.g., soft-decision decoding, bit error probability, or trellis of the codes. On the other hand, coding theory concentrates on the structure of codes based on sophisticated mathematical techniques, with little concern for the decoding complexity, e.g., coset weight distribution, algebraic constructions, or bounds on possible parameters of the codes. In this dissertation, we will present three fundamental topics in coding practice: optimal encoding of linear block codes for bit error probability, trellis structure of linear block codes for trellis-based decoding, and normalized weight of block coded modulation for bandwidth efficient communication systems. The central theme of the thesis is to transform the problems of the above three topics in coding practice into problems in coding theory and to develop the theory associated with the problems. Much of this thesis is devoted to studying what 'optimal' means in different contexts. In summary, we investigated the optimal information bit encoding of a given linear block code for minimizing the probability of an information bit error, with the goal of determining an optimal generator matrix by using the structure of the code. We showed that many natural codes have systematic optimal generator matrices in the quiet region. We analyzed the trellis structure of a self-dual code C to minimize the trellis complexity of the code by considering all equivalent codes of C, with the goal of reducing the soft-decision decoding complexity via permutations on the codeword coordinates. We determined the length/dimension profile of all eight [32, 16, 8] self-dual codes, and find their corresponding optimum permutations. We examined the performance gains achievable by adding interblock memory to block coded modulation systems, with the goal of finding the best codes for normalized distance rather than Hamming distance. We found a large number of best codes for normalized distance for the cases of practical interest.
It is well known that Reed-Muller (RM) codes are not an linear unequal error protec- tion (LUEP) code because the set of minimum-weight vectors span Reed-Muller codes (punctured or not) (1,2). In this paper, we showed that most of RM codes are LUEP codes if RM codes are encoded with recursively decomposed trellis oriented generator ma- trix (TOGM) and maximum-likelihood trellis decod- ing (MLTD) is used. I. INTRODUCTION Uneqaul error protection codes protect some information bits against a great number of errors than other information bits. LUEP codes were first introduced by Masnick and Wolf (3). Boyarinov and Katsman (4) found conditions for linear codes to be LUEP. Let C be and (n, IC, d) linear code. It is shown in (l) that if the minimum-weight vectors of a linear code C does not span it, then C is an LUEP code. It is well known that their set of minimum-weight vectors span RM codes (punctured or not) (2). Therefore, RM codes are not LUEP codes in algebraic decoding. In the soft-decision maxi- mum likelihood decoding, bit-error-rate of RM code depends on the weight distribution of code. If non-systematic GM is used for encoding the RM code and soft-decision maximum likelohood decoding is used in decoding, different set of in- formation bits has a different bit-error-rate since each other has different weight distribution. Therefore, even though RM code is not an LUEP code in algebraci decoding, RM code is an LUEP code in soft-decision maximum likelihood decoding if systematic GM is not used for encoding. Especially, in this paper, LUEP RM codes are constructed by using recursively decomposed TOGM for encoding. Sim- ulations show that bit-error-rate of some information bits is almost twice better than that of the other information bits. By using the recursive decomposition, a simple trellis diagram with parallel structure for the RM code is devised. In ML trellis decoding, information bits are retrieved directly from the labeling of the trellis.
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.