2023/01/13 by Jiun-Hung Yu, Hans-Andrea Loeliger, Hans‐Andrea Loeliger
Computer Science · Engineering · #Cooperative Communication and Network Coding #Coding theory and cryptography #Wireless Communication Security Techniques
paper · pdf · doi:10.1109/tit.2023.3236720
This paper introduces the partial-inverse problem for linearized polynomials and develops its application to decoding Gabidulin codes and lifted Gabidulin codes in linear random network coding. The proposed approach is a natural generalization of its counterpart for ordinary polynomials, thus providing a unified perspective on Reed–Solomon codes for the Hamming metric and for the rank metric. The basic algorithm for solving the partial-inverse problem is a common parent algorithm of a Berlekamp–Massey algorithm, a Euclidean algorithm, and yet another algorithm, all of which are obtained as easy variations of the basic algorithm. Decoding Gabidulin codes can be reduced to the partial-inverse problem via a key equation with a new converse. This paper also develops new algorithms for interpolating crisscross erasures and for joint decoding of errors, erasures, and deviations in random network coding.