Class of nested linear block codes and their decoding algorithm

A new class of nested linear block code is introduced. The codes of this class, referred to as nested codes, cover a wide range of code length and rates. The parity check matrix of a nested code is constructed from two other linear block codes. Although the rates of the resulting codes are not optimal, the codes nevertheless exhibit some useful properties: in particular, they have a well-defined mathematical structure, which leads to a fast and simple decoding algorithm