Improving log-likelihood ratio calculation for LDPC decoding in presence of residual phase noise

Abstract

Abstract In the ever-evolving landscape of communication systems, the primary objective is to ensure efficient and reliable transmission of information across a physical medium, commonly referred to as the channel. The pioneering work of Claude E. Shannon showed that channel coding can harness the full potential of information transfer, enabling the attainment of channel ca pacity. A coding scheme extensively used in digital communication is low-density parity-check (LDPC) codes that provides near-optimal error-correction at low complexity. The most com mon decoding algorithm for LDPC codes is the iterative belief propagation algorithm. This iterative process involves exchanging messages in the form of log-likelihood ratios (LLR), e.g.information about the probability of the decoded bit being either a 0 or a 1. Typically, the LLR calculation assumes an additive white Gaussian noise (AWGN) channel. However, there may be other types of noise affecting the received signal, such as residual phase noise due to imperfect phase estimation. This thesis investigates the performance of LDPC codes if the LLR calculation is extended with the information about phase noise over a single-input single output (SISO) and a 2 × 2 multiple-input multiple-output (MIMO) channel. It is shown that it is possible to extend the conventional LLR calculation to consider phase noise in addition to AWGN and consequently improve the coding gain in the presence of residual phase noise. Hard ware synthesis simulations showed that the proposed PN-LLR scheme significantly increased the hardware resource usage compared to the conventional AWGN-LLR scheme. However, the absolute majority of the increase is attributed to the high cost of divisions in hardware.