Product-matrix (PM) code[1] 

Description

Code constructed using two explicit constructions, with each construction corresponding to one of the two extreme points of the storage-bandwidth trade-off curve [2].

For the MBR point, the parameters of the code are \([n,k, n-1 \ge d\ge k, \alpha, \beta = \frac{\alpha}{d}, M= kd-\binom{k}{2}]\). For the MSR point, the parameters of the code are\([n,k,d \ge 2k-2, \alpha, \beta = \frac{\alpha}{d-k+1}, M=k\alpha]\).

PM codes are the first explicit constructions for all values of the system parameters \([n,k,d]\) at the MBR point, and for all parameters satisfying \([n,k,d \ge 2k-2]\) at the MSR point. Both constructions are based on a common product-matrix frame work which make them easy to implement.

Parent

Cousins

References

[1]
K. V. Rashmi, N. B. Shah, and P. V. Kumar, “Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction”, IEEE Transactions on Information Theory 57, 5227 (2011) DOI
[2]
A. G. Dimakis et al., “Network Coding for Distributed Storage Systems”, IEEE Transactions on Information Theory 56, 4539 (2010) DOI
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Zoo Code ID: product_matrix

Cite as:
“Product-matrix (PM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/product_matrix
BibTeX:
@incollection{eczoo_product_matrix, title={Product-matrix (PM) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/product_matrix} }
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Cite as:

“Product-matrix (PM) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/product_matrix

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/regenerating/product_matrix.yml.