Multi-User SR-LDPC Codes

TL;DR

For certain blocklengths and a sufficiently high number of users, MU-SR-LDPC codes may achieve a higher spectral efficiency than the approximate FBL capacity of the effective single-user Gaussian channel seen by each user in a comparable OMA scheme.

Abstract

This article introduces a novel non-orthogonal multiple access (NOMA) scheme for coordinated uplink channels. The scheme builds on the recently proposed sparse-regression low-density parity-check (SR-LDPC) code, and extends the underlying notions to scenarios with many concurrent users. The resulting scheme, called Multi-User SR-LDPC (MU-SR-LDPC) coding, consists of each user transmitting its own SR-LDPC codeword using a unique sensing matrix in conjunction with a characteristic outer LDPC code. To recover the sent information, the decoder jointly processes the received signals using a low-complexity and highly-parallelizable AMP-BP algorithm. At finite blocklengths (FBL), MU-SR-LDPC codes are shown to achieve a target BER at a higher spectral efficiency than baseline orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) schemes with similar computational complexity. Furthermore, MU-SR-LDPC codes are shown to match the performance of maximum a posteriori (MAP) decoding in certain regimes. For certain blocklengths and a sufficiently high number of users, MU-SR-LDPC codes may achieve a higher spectral efficiency than the approximate FBL capacity of the effective single-user Gaussian channel seen by each user in a comparable OMA scheme. Results are supported by numerical simulations.

Figures (4)

• Figure 1: This figure depicts the encoding process for a single user in a MU-SR-LDPC system. Information messages are first encoded using a NB-LDPC code, then each coded symbol is transformed into a one-sparse index vector. The set of index vectors is then vertically concatenated and the resultant vector is pre-multiplied by the sensing matrix $\mathbf{A}$ to obtain an SR-LDPC codeword.
• Figure 2: This figure provides a graphical representation of the proposed AMP-BP recovery algorithm which seeks to recover $\{\mathbf{s}_k : k \in [K]\}$ from the vector of noisy observations $\mathbf{y}$. The algorithm begins by computing a residual error enhanced with an Onsager correction term using all $K$ current state estimates. Then, each state estimate is refined based on the residual error and denoised by running a few rounds of BP on the factor graph of the outer LDPC code. The process then repeats itself until stopping conditions have been met.
• Figure 3: This figure compares the BER performance of four candidate multiple access schemes: OMA with 5G-NR LDPC codes, OMA with SR-LDPC codes, IDMA with LDPC codes, and MU-SR-LDPC codes. In each case, there are $K = 2$ active users who each wish to transmit $B = 584$ information bits over $n = 1460$ channel uses (r.d.o.f.). This MU-SR-LDPC code requires a $0.3-0.5$dB lower SNR to achieve a target BER of $10^{-3}$ than its competitors.
• Figure 4: This figure plots the BER as a function of $R_{\mathrm{sum}}$ for the MU-SR-LDPC scheme under consideration at $E_b/N_0 = 3$dB. This figure shows that MU-SR-LDPC coding achieves a higher spectral efficiency than its competitors. Furthermore, the spectral efficiency of MU-SR-LDPC coding appears to increase with $K$.