B-code[1] 

Description

The first array code, constructed over \(GF(q)\).

Decoding

Efficient decoding algorithm against erasures [1].

Parent

Cousins

  • Reed-Solomon (RS) code — B-codes can be interpreted as RS codes over polynomials whose symbols lie in Galois rings [1,2].
  • 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 [2].

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]
J. L. Fan, “Array Codes as LDPC Codes”, Constrained Coding and Soft Iterative Decoding 195 (2001) 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/tree/main/codes/classical/matrices/raid/b_array.yml.