List and unique error-erasure decoding of interleaved Gabidulin codes with interpolation techniques

Abstract-A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate R ∈ [0, 1]. An efficient interpolation-based decoding algorithm for this code construction is given which allows to correct insertions and deletions up to the normalized radius s (1 − ((1/h + h)/(h − s + 1))R), where h is the folding parameter and s ≤ h is a decoding parameter. The algorithm serves as a list decoder or as a probabilistic unique decoder that outputs a unique solution with high probability. An upper bound on the average list size of (folded) subspace codes and on the decoding failure probability is derived. A major benefit of the decoding scheme is that it enables probabilistic unique decoding up to the list decoding radius.

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“…The receiver knows n r , the code parameter k and the decoding parameter s and can compute the degree restriction D in (8).…”

Section: Lemma 2 a Nonzero Polynomial Fulfilling The Interpolation Comentioning

confidence: 99%

“…The probability to get a unique solution is then equal to the probability to get a weight k codeword. Since similar to [6] and [8] we assume that the coefficients of B The probability that one B…”

Section: Lemmamentioning

confidence: 99%

List and probabilistic unique decoding of folded subspace codes

Bartz

Sidorenko

2015

2015 IEEE International Symposium on Information Theory (ISIT)

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“…)+k−1} must hold, which contradicts (16). Lemma 4 shows that there is a unique solution to (14) if rk(Q nr−τ −k ) = s. Clearly, Q nr−τ −k contains the leading coefficients of Q for some ℓ that are contained in T nr,j and j ∈ [1, s].…”

Section: Efficient Interpolationmentioning

confidence: 96%

“…This decoder is not a polynomial-time list decoder but it provides the basis of the list with quadratic complexity. The derivation of the maximum and average list size is similar to [16].…”

Section: A List Decoding Approachmentioning

confidence: 99%

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Efficient interpolation-based decoding of interleaved subspace and Gabidulin codes

Bartz

Wachter-Zeh

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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An interpolation-based decoding scheme for interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond half the minimum subspace distance. Further, an efficient interpolation procedure for the required linearized multivariate polynomials is presented and a computationally-and memory-efficient root-finding algorithm for the probabilistic unique decoder is proposed. These two efficient algorithms can also be applied for accelerating the decoding of interleaved Gabidulin codes.

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