Abstract: A method of and apparatus for providing error correction coding for a block of user data in which the user data is initially modulated by a first modulator and then the modulated user data is error correction encoded to produce a first plurality of check bits. The first plurality of check bits are then modulated by a second modulator whose output is then fed to a second error correction encoder which produces a second plurality of check bits. The modulated user data, the first plurality of check bits and the second plurality of check bits are all fed to a shift register where the error correction encoded user data block is formed, useful with magnetic and optical storage devices.

Abstract: A method and apparatus for providing maximum rate modulation or compression encoding and decoding for use with magnetic and optical recording and optical fiber communications is disclosed in which primarily two algorithms are utilized which satisfy the conditions that encoding and decoding require only a small constant number of elementary operations, without multiplications or divisions and that only a small amount of memory space for a small number of integers is required. Thus, the present invention operates with only linear time complexity and only linear memory complexity. The invention utilizes a direct enumeration algorithm to accomplish a mapping and an inverse enumeration algorithm to accomplish an inverse mapping back to enumeration.