US Patent 9407398 System and method using cascaded single partity check coding

A system and method including a parity bit encoder for encoding each n−3 bits of data to be transmitted with three parity check bits to produce blocks of n bits (n−3 information bits plus three parity bits associated with the n information bits). Each of the blocks of n bits are Gray mapped to three QAM symbols that are modulated onto an optical wavelength and transmitted to a receiver. A maximum a posteriori (MAP) decoder is used at the receiver to correct for cycle slip.