Irregular π-rotation LDPC codes

We present irregular π-rotation LDPC codes by extending the classic π-rotation parity check matrix to allow irregular column weight and choice of many code rates. The irregular π-rotation codes are defined with a small set of parameters providing the exact definition of the code with its performance. The encoding circuit is based on the original π-rotation design and thus users have the choice of using regular or irregular matrix patterns and various code rates without changing the encoding circuitry. We compare the performance of the irregular π-rotation code against the binary Shannon limit for several rates.