A generalized LDPC decoder for blind turbo equalization

Abstract

The equations for iteratively decoding low-density parity-check (LDPC) codes are generalized to compute joint probabilities of arbitrary sets of codeword bits and parity checks. The standard iterative LDPC decoder, which computes single variable probabilities, is realized as a special case. Another specialization allows pairwise joint posterior probabilities of pairs of codeword bits to be computed. These pairwise joint probabilities are used in an expectation-maximization (EM) based blind channel estimator that is ignorant of the code constraints. Channel estimates are input to a turbo equalizer that exploits the structure of the LDPC code. Feeding pairwise posterior probabilities back to the channel estimator eliminates the need to average across time for channel estimation. Therefore, this scheme can be used to equalize very long codewords, even when the channel is time varying. This blind turbo equalizer is evaluated through computer simulations and found to perform as well as a channel-informed turbo equalizer but with approximately twice the number of turbo iterations.