On Design of Protograph LDPC Codes for Large-Scale MIMO Systems

Abstract

Protograph low-density parity-check (LDPC) codes and large-scale multi-input multi-output (LS-MIMO) systems have achieved great interest with various practical applications. However, how to effectively evaluate and design protograph LDPC codes for LS-MIMO systems remains a challenging yet critical problem, especially for low-latency applications. To solve that design challenge, the protograph extrinsic information transfer chart (PEXIT) algorithm for LS-MIMO systems, so-called LS-MIMO-PEXIT algorithm, is first derived based on the mutual information functions of messages that are passed on the joint MIMO detection and LDPC decoding graph. The proposed LS-MIMO-PEXIT algorithm plays a vital role in the optimization process of designing new protograph LDPC codes, tailored for LS-MIMO communications systems. Experiment results demonstrate that the analytical results based on the LS-MIMO-PEXIT algorithm are in good agreement with the simulation results under various input constraints, including the coding rate, the number of decoding iterations, and the LS-MIMO configuration. On top of that, the new protograph LDPC codes designed using our LS-MIMO-PEXIT algorithm achieve a coding gain from 0.2 dB at a low coding rate to 0.4 dB at a high coding rate in comparison with the state-of-the-art protograph codes in the literature. Additionally, we incorporate the practical design experience and the theoretical analysis of mutual functions into a two-step procedure to search for protograph LDPC codes that do not have error-floor behavior at frame error rate (FER) or bit error rate (BER) as low as 10 −5 or 10 −7 , respectively. Together with the coding gain, the error-floor-free feature of the proposed protograph LDPC codes is vitally important for future wireless networks where the ultra-reliability is one of the critical requirements. INDEX TERMS Large-scale multiple-input multiple-output (LS-MIMO), protograph low-density paritycheck (LDPC) codes, channel coding, protograph extrinsic information transfer chart, iterative decoding threshold, low latency.

Protograph LDPC Code Design For LS-MIMO 1-bit ADC Systems

“…Next, we pick two protograph LDPC codes from the literature to compare with our new codes -AR3A codes [28] (punctured codes) and the protograph LDPC codes previously optimized for LS-MIMO channels and joint double-layer belief propagation receiver [19] (NND codes). The reason behind this choice is that the AR3A codes have three checks, the same as the number of checks of our proposed codes.…”

“…The AR3A codes were reported to achieve the best performance in the fading environment [28]. Also, the NND codes [19] are chosen since they are the only codes, to our best understanding, that satisfies two conditions: 1) belong to non-punctured class; 2) have the same check and were optimized for low-resolution ADC with a fixed number of decoding iterations. Those two conditions are required to achieve a fair comparison with our proposed codes.…”

“…The joint MIMO detection and protograph LDPC decoding algorithm, [13,19], is a promising solution for the massive MIMO coded communication systems because of two main reasons:…”

“…Moreover, Nguyen et al [13] and Vu et al [19] employed similar ideas in the joint belief propagation decoder for large-scale MIMO coded communication systems to analyze the performance of low-resolution ADCs (from 2-bit to 5-bit).…”

“…The proto-matrices of the new protograph LDPC codes optimized for a maximum number of decoding iterations are 50 and 10 × 10 MIMO configurations, are presented in Section 4. Here, the protograph LDPC codes for massive MIMO channel [19], and the new optimized protograph LDPC codes are chosen to perform FER performance analysis. Finally, Section 5 concludes the paper.…”