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B-code[1]

Description

The first array code, constructed over \(GF(q)\). See [2] for more details.

Decoding

Efficient decoding algorithm against erasures [1].

Cousins

  • Reed-Solomon (RS) code— B-codes can be interpreted as RS codes over polynomials whose symbols lie in Galois rings [1,3].
  • Array-based LDPC (AB-LDPC) code— AB-LDPC codes are constructed from certain classes of B-codes. B-codes can be viewed as binary codes by mapping their ring elements to permutation matrices (cf. lifting). The resulting codes turn out to be LDPC [3].

Member of code lists

Primary Hierarchy

Classical Domain
Matrix Kingdom
Matrix-based codeECC
Array codeDistributed-storage ECC
MDS array code
Parents
MDS array code
B-codes are examples of MDS array codes [4].
B-code

References

[1]
M. Blaum and R. M. Roth, “New array codes for multiple phased burst correction”, IEEE Transactions on Information Theory 39, 66 (1993) DOI
[2]
M. Blaum, P. G. Farrell, H. C. A. van Tilborg, 1998. Array codes. Handbook of coding theory, 2 (Part 2), pp. 1855-1909.
[3]
J. L. Fan, “Array Codes as LDPC Codes”, Constrained Coding and Soft Iterative Decoding 195 (2001) DOI
[4]
I. Tamo, Z. Wang, and J. Bruck, “Zigzag Codes: MDS Array Codes With Optimal Rebuilding”, IEEE Transactions on Information Theory 59, 1597 (2013) arXiv:1112.0371 DOI
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Zoo Code ID: b_array

Cite as:
“B-code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/b_array
BibTeX:
@incollection{eczoo_b_array, title={B-code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/b_array} }
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Permanent link:
https://errorcorrectionzoo.org/c/b_array

Cite as:

“B-code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/b_array

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/raid/mds_array/b_array.yml.