Algebraic List-decoding of Subspace Codes
Hessam Mahdavifar, Alexander Vardy

TL;DR
This paper develops an algebraic list-decoding method for Koetter-Kschischang subspace codes, significantly improving error correction capabilities in network coding by generalizing existing constructions and achieving higher decoding radii.
Contribution
It introduces a novel algebraic list-decoding algorithm for subspace codes, extending Koetter-Kschischang codes and surpassing previous error correction bounds.
Findings
Achieves successful list-decoding up to a higher error radius than previous bounds.
Generalizes Koetter-Kschischang construction for improved decoding.
Provides theoretical guarantees for decoding performance at various rates.
Abstract
Subspace codes were introduced in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). Subspace codes are indeed collections of subspaces of a certain vector space over a finite field. The Koetter-Kschischang construction of subspace codes are similar to Reed-Solomon codes in that codewords are obtained by evaluating certain (linearized) polynomials. In this paper, we consider the problem of list-decoding the Koetter-Kschischang subspace codes. In a sense, we are able to achieve for these codes what Sudan was able to achieve for Reed-Solomon codes. In order to do so, we have to modify and generalize the original Koetter-Kschischang construction in many important respects. The end result is this: for any integer , our list- decoder guarantees successful recovery of the message subspace provided…
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Advanced Wireless Communication Technologies
