Disclosed are an encoding apparatus for a quasi-cyclic low-density parity check code for calculating r\xd7m-bit redundant data for information data of length k\xd7m bits, and a cyclic addition apparatus including a k\xd7m-bit shift register and exclusive OR. The receiver includes an analysis engine, coupled to receive the packet from the network and adapted to parse and validate the header, locate the connection context, and generate a classification of the header. At least one of the opposed edges overhangs an undercut region of the micromachined crystalline structure by an overhang distance that is greater than one third of the width.