Approximated EM Algorithms for Estimation of Unknown Coded Discrete Memoryless Channels

Mismatch between the true channel and the channel assumed in the design of a communication system can degrade system performance. Joint channel estimation and data recovery via the Expectation-Maximization (EM) algorithm can overcome this problem. Though stable, the EM algorithm can be complex to implement and can exhibit slow convergence. We present approximations of the EM algorithm that reduce computational complexity and accelerate convergence for LDPC-coded discrete memoryless channels. In place of the exact bit-wise maximum a posteriori probability decoder in the E step of the EM algorithm, we use the sum-product decoder and min-sum decoder. In the M step, we use hard information instead of soft information to estimate the channel parameter. In order to evaluate the approximations in a practical channel mismatch scenario, we use a flash memory channel described by a quantized Normal-Laplace mixture model. The simulation results demonstrate that the approximations in the E step can estimate the true channel with low-complexity decoding and those in the M step can accelerate the convergence with reduced measurement precision.