Iterative LMMSE channel estimation and decoding based on probabilistic bias

Iterative channel estimation and decoding based on probabilistic bias is investigated. In order to control the occurrence probability of transmitted symbols, biased convolutional codes (CCs) are proposed. A biased CC is obtained by puncturing the parity bit of a conventional (unbiased) CC and by inserting a fixed bit at the punctured position when the state is contained in a certain subset of all possible states. A priori information about the imposed bias is utilized for the initial linear minimum mean-squared error (LMMSE) channel estimation. This paper focuses on biased turbo codes that are constructed as the parallel concatenation of two biased CCs with interleaving, and proposes an iterative LMMSE channel estimation and decoding scheme based on approximate belief propagation. The convergence property of the iterative LMMSE channel estimation and decoding scheme is analyzed via density evolution (DE). The DE analysis allows one to design the magnitude of the bias according to the coherence time, in terms of the decoding threshold. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in the moderate signal-to-noise ratio (SNR) regime, at the expense of a performance degradation in the high SNR regime