Lattice-Code Multiple Access: Architecture and Efficient Algorithms

TL;DR

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.

Abstract

This paper studies a $K$-user lattice-code based multiple-access (LCMA) scheme. Each user equipment (UE) encode its message with a practical lattice code, where we suggest a $2^m$-ary \emph{ring code} with symbol-wise bijective mapping to $2^m$-PAM. The coded-modulated signal is spread with its designated signature sequence, and all $K$ UEs transmit simultaneously. The LCMA receiver choose some integer coefficients, computes the associated $K$ streams of \emph{integer linear combinations} (ILCs) of the UEs' messages, and then reconstruct all UEs' messages from these ILC streams. To execute this, we put forth new efficient LCMA \emph{soft detection} algorithms, which calculate the a posteriori probability of the ILC over the lattice. The complexity is of order no greater than $O(K)$, suitable for massive access of a large $K$. The soft detection outputs are forwarded to $K$ ring-code decoders, which employ $2^m$-ary belief propagation to recover the ILC streams. To identify the optimal integer coefficients of the ILCs, a new ``%\emph{bounded independent vectors problem}" (BIVP) is established. We then solve this BIVP by developing a new \emph{rate-constraint sphere decoding} algorithm, significantly outperforming existing LLL and HKZ lattice reduction methods. Then, we develop optimized signature sequences of LCMA using a new target-switching steepest descent algorithm. With our developed algorithms, LCMA is shown to support a significantly higher load of UEs and exhibits dramatically improved error rate performance over state-of-the-art multiple access schemes such as interleave-division multiple-access (IDMA) and sparse-code multiple-access (SCMA). The advances are achieved with just parallel processing and $K$ single-user decoding operations, avoiding the implementation issues of successive interference cancelation and iterative detection.

Figures (10)

• Figure 1: Block diagram of the transmitters and receiver of a LCMA system. All users utilize the same $2^{m}$-ary RCM. No interleavers and deinterleavers are used. For each MA channel realization, the optimized coefficient matrix $\mathbf{A}$ is identified by solving the BIVP w.r.t. the channel state information. The LCMA soft detection and decoding of the $K$ streams are implemented in parallel.
• Figure 2: Averages NMSE with the proposed RS-SD, $N=8,K=24$. The channel coefficients follows Rayleigh distribution.
• Figure 3: Achievable symmetric rate per-user of LCMA with our designed spreading matrix $\mathbf{S}$ in Gaussian MA channel, where $N_S=8,K=$16 and 24. Total power constraint is utilized here. Note that the horizontal axis denotes the per-user SNR, while the vertical axis denotes the per-user rate. The sum-rate is equal to $K$ times the per-user rate.
• Figure 4: BER of LCMA in Gaussian MA channel with $N_{s}=8$. BPSK and a rate 1/2 LDPC code of length $k=3840$ are utilized. The individual power constraint is utilized in designing the spreading matrix $\mathbf{S}$.
• Figure 5: BLER of LCMA with QPSK in fading MAC, $N=4$.

Theorems & Definitions (6)

• Definition 1
• Remark 1
• Definition 2
• Theorem 1
• proof : Proof of Theorem 1
• Remark 2