Systems and methods for reduced power multi-layer data decoding

A storage device, the storage device comprising:

• a data encoder circuit operable to apply an encoding algorithm to an input data set in accordance with a multi-layer code structure including a first row and a last row to yield an encoded data set, wherein the last row of the multi-layer code structure represented in the encoded data set conforms to an identity matrix;
• a storage medium operable receive a data set corresponding to the encoded data set;
• a head assembly disposed in relation to the storage medium and operable to provide a sensed signal corresponding to the encoded data set;
• a read channel circuit including:
• an analog to digital converter circuit operable to sample an analog signal derived from the sensed signal to yield a series of digital samples;
• an equalizer circuit operable to equalize the digital samples to yield detector data set corresponding to the encoded data set;
• a data detector circuit operable to apply a data detection algorithm to the data set to yield a detected output;
• a data decoder circuit operable to:
• add a second decoded output from the decoder input to yield a first summed output;
• shift the summed output to conform with the identity matrix to yield a shifted output;
• subtract a third decoded output from the shifted output to yield a second summed output;
• and wherein the first summed output is provided unshifted as an output codeword.