B-code[1]
Description
The first array code, constructed over \(GF(q)\). See [2] for more details.
Decoding
Efficient decoding algorithm against erasures [1].
Parent
- MDS array code — B-codes are examples of MDS array codes [3].
Cousins
- Reed-Solomon (RS) code — B-codes can be interpreted as RS codes over polynomials whose symbols lie in Galois rings [1,4].
- 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 [4].
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]
- 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
- [4]
- J. L. Fan, “Array Codes as LDPC Codes”, Constrained Coding and Soft Iterative Decoding 195 (2001) DOI
Page edit log
- Victor V. Albert (2023-05-04) — most recent
Cite as:
“B-code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/b_array