Systems and methods for encoding and decoding check-irregular non-systematic IRA codes of messages in any communication or electronic system where capacity achieving coding is desired. According to these systems and methods, IRA coding strategies, including ones that employ capacity-approaching non-systematic IRA codes that are irregular and that exhibit a low error floor, are employed. These non-systematic IRA codes are particularly advantageous in scenarios in which up to half of coded bits could be lost due to channel impairments and/or where complementary coded bits are desired to transmit over two or more communications sub-channels. An encoder includes information bit repeaters and encoders, one or more interleavers, check node combiners, a check node by-pass and an accumulator. A decoder includes a demapper, one or more check node processors, an accumulator decoder, a bit decoder, and one or more interleavers/deinterleavers.