3 research outputs found
Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases
An interpolation-based decoding scheme for L-interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a polynomial-time probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond
half the minimum subspace distance. Both schemes can decode γ insertions
and δ deletions up to γ + Lδ ≤ L(nt − k), where nt is the dimension of the
transmitted subspace and k is the number of data symbols from the field Fqm.
Further, a complementary decoding approach is presented which corrects γ insertions and δ deletions up to Lγ +δ ≤ L(nt −k). Both schemes use properties
of minimal Gr¨obner bases for the interpolation module that allow predicting
the worst-case list size right after the interpolation step. An efficient procedure for constructing the required minimal Gr¨obner basis using the general
K¨otter interpolation is presented. A computationally- and memory-efficient
root-finding algorithm for the probabilistic unique decoder is proposed. The
overall complexity of the decoding algorithm is at most O(L2n2 r) operations in
F
qm where nr is the dimension of the received subspace and L is the interleaving order. The analysis as well as the efficient algorithms can also be applied
for accelerating the decoding of interleaved Gabidulin codes
Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases
An interpolation-based decoding scheme for L-interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a polynomial-time probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond
half the minimum subspace distance. Both schemes can decode γ insertions
and δ deletions up to γ + Lδ ≤ L(nt − k), where nt is the dimension of the
transmitted subspace and k is the number of data symbols from the field Fqm.
Further, a complementary decoding approach is presented which corrects γ insertions and δ deletions up to Lγ +δ ≤ L(nt −k). Both schemes use properties
of minimal Gr¨obner bases for the interpolation module that allow predicting
the worst-case list size right after the interpolation step. An efficient procedure for constructing the required minimal Gr¨obner basis using the general
K¨otter interpolation is presented. A computationally- and memory-efficient
root-finding algorithm for the probabilistic unique decoder is proposed. The
overall complexity of the decoding algorithm is at most O(L2n2 r) operations in
F
qm where nr is the dimension of the received subspace and L is the interleaving order. The analysis as well as the efficient algorithms can also be applied
for accelerating the decoding of interleaved Gabidulin codes