Papers for
digital communication developers
Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.
Reed solomon decoding methods correct more insertion and deletion errors
Insdel Reed-Solomon Decoding Algorithms up to the Half-Singleton Bound
Abstract: In this paper, we focus on decoding optimal Reed-Solomon codes of dimension two for insdel errors up to the half-Singleton bound. We present a decoding algorithm for the general insertion-and-deletion scenario with a time complexity smaller than brute-force decoding. Our algorithm corrects insdel errors up to the half-Singleton bound, which exceeds the scope of existing methods. Additionally, for the special cases of insertion-only and deletion-only insdel error patterns, we present two different algorithms with a time complexity smaller than our general algorithm.
Linear codes proven to meet coverage bounds up to redundancy fourteen
Auxiliary Codes and the Generalized Packing-Covering Conjecture
Abstract: The generalized packing--covering conjecture asks whether, at every order, the packing radius of a linear code is at most its covering radius. We prove the conjecture for every linear code of redundancy at most fourteen over every finite field, extending the previously established redundancy-seven range. We also prove the generalized Hamming-weight bound $d_t(C)\le2R_t(C)+1$ whenever the alphabet size $q$ satisfies $q\ge R_t(C)$, using an auxiliary-code criterion that converts a syndrome-space covering property into a weight bound. For binary primitive BCH codes, the packing radius is strictly smaller than the covering radius for every fixed error parameter and order, both at least two, once the extension degree is sufficiently large; this follows from existing covering bounds.