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Suboptimal Decoding of Linear Codes

Ilya I. Dumer

Springer eBooksJan 1, 19939 citations

Soft decoding performance of extremal self-dual codes

V.K. Bhargava

Performance of soft decoded extremal self-dual codes of lengths 8 to 72 are obtained over the Gaussian channel. The results indicate that for decoded bit-error rates below 10-3, which is the main region of interest for coding application, substantial coding gains can be obtained by using extremal self-dual codes.

Proceedings of the IEEEJan 1, 19830 citations

Projection Decoding of Some Binary Optimal Linear Codes of Lengths 36 and 40

Lucky Galvez, Jon-Lark Kim

Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes, such as cyclic codes, Reed–Solomon codes, and Reed–Muller codes, have nice decoding algorithms. However, many optimal linear codes do not have an efficient decoding algorithm except for the general syndrome decoding which requires a lot of memory. Therefore, a natural question to ask is which optimal linear codes have an efficient decoding. We show that two binary optimal [ 36 , 19 , 8 ] linear codes and two binary optimal [ 40 , 22 , 8 ] codes have an efficient decoding algorithm. There was no known efficient decoding algorithm for the binary optimal [ 36 , 19 , 8 ] and [ 40 , 22 , 8 ] codes. We project them onto the much shorter length linear [ 9 , 5 , 4 ] and [ 10 , 6 , 4 ] codes over G F ( 4 ) , respectively. This decoding algorithm, called projection decoding, can correct errors of weight up to 3. These [ 36 , 19 , 8 ] and [ 40 , 22 , 8 ] codes respectively have more codewords than any optimal self-dual [ 36 , 18 , 8 ] and [ 40 , 20 , 8 ] codes for given length and minimum weight, implying that these codes are more practical.Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes, such as cyclic codes, Reed–Solomon codes, and Reed–Muller codes, have nice decoding algorithms. However, many optimal linear codes do not have an efficient decoding algorithm except for the general syndrome decoding which requires a lot of memory. Therefore, a natural question to ask is which optimal linear codes have an efficient decoding. We show that two binary optimal [ 36 , 19 , 8 ] linear codes and two binary optimal [ 40 , 22 , 8 ] codes have an efficient decoding algorithm. There was no known efficient decoding algorithm for the binary optimal [ 36 , 19 , 8 ] and [ 40 , 22 , 8 ] codes. We project them onto the much shorter length linear [ 9 , 5 , 4 ] and [ 10 , 6 , 4 ] codes over G F ( 4 ) , respectively. This decoding algorithm, called projection decoding, can correct errors of weight up to 3. These [ 36 , 19 , 8 ] and [ 40 , 22 , 8 ] codes respectively have more codewords than any optimal self-dual [ 36 , 18 , 8 ] and [ 40 , 20 , 8 ] codes for given length and minimum weight, implying that these codes are more practical.

arXiv:1911.07212MathematicsDec 19, 20191 citation

The decoding of binary quasi-cyclic codes

P. Heijnen, Henk C. A. van Tilborg

Jan 1, 19984 citations

Construction and decoding of matrix-product codes from nested codes

Fernando Hernando, Kristine Lally, Diego Ruano

Applicable Algebra in Engineering Communication and ComputingOct 8, 200959 citations

Performance of extremal codes

Anton Malevich

Assume that a binary linear code is transmitted over a channel with the symbol error probability p and that bounded distance decoding is used. In this case it is known [3] that for sufficiently small p the performance of the code is only a question of the weight distribution (weight enumerators of more efficient codes are lexicographically smaller). Based on this result we study the efficiency of extremal self-dual codes. Extremal doubly-even codes have unique weight enumerators for each length, and at first glance it may seem that these codes should perform worse than other codes with the same minimum distance. However we show that this is not always the case when comparing to singly-even codes. We also show that a doubly-even code may perform better than a non self-dual code. We find the most efficient codes among extremal singly-even codes of length 24m + 8 and 24m + 16. We also consider some families of extremal singly-even codes with uniquely determined weight enumerators (s-extremal codes, codes with minimal shadow). It appears that they always perform better than extremal doublyeven codes of the same length. The results are joint work with Wolfgang Willems (Magdeburg).Assume that a binary linear code is transmitted over a channel with the symbol error probability p and that bounded distance decoding is used. In this case it is known [3] that for sufficiently small p the performance of the code is only a question of the weight distribution (weight enumerators of more efficient codes are lexicographically smaller). Based on this result we study the efficiency of extremal self-dual codes. Extremal doubly-even codes have unique weight enumerators for each length, and at first glance it may seem that these codes should perform worse than other codes with the same minimum distance. However we show that this is not always the case when comparing to singly-even codes. We also show that a doubly-even code may perform better than a non self-dual code. We find the most efficient codes among extremal singly-even codes of length 24m + 8 and 24m + 16. We also consider some families of extremal singly-even codes with uniquely determined weight enumerators (s-extremal codes, codes with minimal shadow). It appears that they always perform better than extremal doublyeven codes of the same length. The results are joint work with Wolfgang Willems (Magdeburg).

Jan 1, 20060 citations

A projection decoding of a binary extremal self-dual code of length 40

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