Systems and methods for advanced iterative decoding and channel estimation of concatenated coding systems

A system for decoding codes of length N that include a message of K bits using soft-input soft-output (SISO) message passing decoding for a number of iterations IT>1 and a number of parity check matrices P comprising:

• a de-mapper configured to receive a modulation signal comprising symbols, and to convert the modulation signal into bit log-likelihood ratios;
• and
• at least one decoder coupled to the de-mapper, wherein the at least one decoder is configured to receive the bit log-likelihood ratios and generate a decoded signal comprising bits, and wherein the at least one decoder is configured to:
• a. identify a number of sign disagreement positions Q≦N−K on hard decisions of said P sequences of bit log-likelihood ratios that identify possible bit error positions and wherein N−K is a set of check nodes,
• b. generate P new parity check matrices such that the sparse columns include N−K columns corresponding to said number of Q≦N−K sign disagreement positions and, on the condition that Q<N−K, up to N−K−Q sparse columns correspond to different combinations of N−K−Q of N−K−Q+R least reliable said updated P sequences of bit log-likelihood ratios, wherein R≧P is a configurable integer associated with R least reliable bits,
• c. decode said updated log-likelihood ratios using said plurality of P new parity check matrices to produce further updated log-likelihood ratios, employing soft-input soft-output (SISO) message passing decoding until a desired number of iterations is reached or until decoding using at least one of said P new parity check matrices produces a valid codeword,
• d. on the condition that said decoding using said plurality of P parity check matrices produces no valid codeword, perform additional decoding that is based at least in part on algebraic decoding of the sequences of said further updated log-likelihood ratios;
• and
• e. output the generated decoded signal.