In view of the high computational complexity of traditional linear equalization algorithms in Orthogonal Time Frequency Space (OTFS) systems, a minimum mean square error (MMSE) channel equalization algorithm based on Matrix Chunking Lower and Upper Triangular Decomposition (CLU) is proposed. The proposed algorithm derives the structural properties of the chunked MMSE equalization matrix by leveraging the block diagonal structure of the Cyclic Prefix OTFS (CP-OTFS) time-domain channel matrix and the quasi-band structure of its constituent block matrices. On this basis, triangular decomposition combined with forward and backward substitution is used to avoid matrix inversion. This approach significantly reduces the complexity of the MMSE algorithm without sacrificing its performance.

This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check (RL-RC-SC-LDPC) codes from RL-RC-LDPC block codes. There are two important keys. One is the performance of the base matrix. RL-LDPC codes have been adopted in the technical specification of 5G new radio (5G-NR). We use the 5G NR LDPC code as the base matrix. The other is the edge coupling design. In this regard, we have designed a rate-compatible coupling algorithm, which can improve performance under multiple code rates. The constructed RL-RC-SC-LDPC code property requires a large coupling length L and thus we improved the reciprocal channel approximation (RCA) algorithm and proposed a sliding window RCA algorithm. It can provide lower complexity and latency than RCA algorithm. The code family shows improved thresholds close to the Shannon limit and finite-length performance compared with 5G NR LDPC codes for the additive white Gaussian noise (AWGN) channel.