Multilevel Coding Scheme for Integer-Forcing MIMO Receivers With Binary Codes

Abstract

An integer-forcing (IF) linear multiple-input multiple-output (MIMO) receiver has recently been proposed, which is theoretically shown to achieve near capacity with almost the same complexity as that of conventional linear receivers. The key idea is that the receiver attempts to directly decode integer-linear combinations of codewords. To ensure that this sum-decoding operation is feasible, in previous works, lattice codes over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{q}$ </tex-math></inline-formula> were employed. Although those codes can attain good theoretical performance, however, its implementation complexity can be considerably high in practice, especially when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> is large to support high-order modulations. In this paper, we propose a practical multilevel coding scheme for IF MIMO, in which multilevel encoding composed of binary linear codes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(q = 2)$ </tex-math></inline-formula> in conjunction with the natural mapping is employed on the transmitter side and multistage decoding adapted to the IF operation is employed on the receiver side. The performance of the proposed scheme is extensively evaluated both analytically and numerically, showing that the gain of IF over conventional receivers is indeed achievable in practical settings with almost the same complexity. Our results imply that the proposed IF MIMO can be an attractive solution for the 5G communications due to its ability of supporting high spectral efficiency with low complexity.