Lattice-Code Multiple Access: Architecture and Efficient Algorithms

This paper proposes a lattice-code multiple-access (LCMA) scheme for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula>-user uplink systems. Each user encodes messages via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{m}$</tex-math></inline-formula>-ary lattice codes mapped to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^{m}$</tex-math></inline-formula>-PAM. The receiver employs integer coefficients to compute <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integer linear combinations</i> (ILCs) of messages, then reconstructs original data through novel low-complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">soft detection</i> and single-user decoders. Key contributions include: 1) A soft detector calculating a posteriori probabilities of ILCs over lattices, enabling efficient belief-propagation decoding; 2) A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bounded independent vectors problem</i> (BIVP) framework to optimize ILC coefficients, solved by a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate-constrained sphere decoder</i> outperforming traditional lattice reduction methods; 3) Optimized signature sequences designed via a targetswitching steepest descent algorithm. Simulations demonstrate LCMA's superiority over IDMA and SCMA in supporting higher user loads and achieving lower error rates, while avoiding successive interference cancellation or iterative detection.