Algebraic Structure and Decoding of Two-Dimensional Cascade Codes
Keith Saints, Chris Heegard · 2005
This paper discusses the algebraic structure of cascaded Reed-Solomon (CRS) codes, and presents an algorithm for decoding them. A CRS code is a cascade (or "generalized concatenated" ) code constructed using Reed-Solomon codes as component codes. In particular, we consider hyperbolic CRS (HCRS) codes: these are CRS codes designed to have the minimum distance given by the cascade code bound. Compared to Reed-Solomon codes over the same alphabet, HCRS codes have longer block-lengths. Compared to other two dimensional cyclic codes (products of Reed-Solomon codes, duals of such products, and codes proposed by Sakata [1]) with the same minimum distance, HCRS codes have higher rates.