An Algebraic Construction of Linear Codes with Exponential Error Bounds on Regular Channels
Tomohiko Uyematsu, Eiji Okamoto · International Symposium on Information Theory and its Applications · 1994
This paper proposes an explicit construction of codes achieving Shannon's capacity for a regular channel with an input alphabet of 2m symbols. The proposed codes are obtained by applying the idea of variable concatenation to a class of generalized concatenated codes proposed by Hirasawa et al. with employing algebraic geometry codes as outer codes. Further, we clarify that the error exponent of the proposed code is the largest among those of the algebraic codes with explicit constructions, and exceeds the error exponent obtained by Forney for concatenated codes.