Elsevier

Physical Communication

Volume 3, Issue 3, September 2010, Pages 147-155
Physical Communication

Full length article
Performance analysis of superposition coded modulation

https://doi.org/10.1016/j.phycom.2009.08.008Get rights and content

Abstract

This paper presents a comprehensive analysis of superposition coded modulation (SCM). Two types of SCM schemes, i.e., the single-code SCM (SC-SCM) and multi-code SCM (MC-SCM), are analyzed. The basic features of SCM are described, followed by the information-theoretic analysis. Different encoding/decoding strategies are compared from the capacity point of view. A semi-analytical evolution technique is proposed to track the convergence behavior of iterative decoding. Analytical error-rate analysis is then conducted to predict the asymptotic performance. Numerous examples demonstrate that the analysis tools discussed in this paper can provide reasonably accurate performance prediction for SCM schemes.

Introduction

Superposition coded modulation (SCM) is a high-rate transmission scheme in which the transmit signal xi is a weighted sum of K coded symbols {xi,1,xi,2,,xi,K}, i.e., xi=k=1Kβkxi,k, where each xi,k is drawn from a binary phase-shift keying (BPSK) constellation [1], [2], [3], [4], [5], [6], [7], [8] and {βk} are a set of weighting constants. We will call {xi,k:i=1,2,} collectively as the kth layer. A K-layer SCM is defined over a size-2K constellation.

A distinctive property of SCM is that it can be formed by naturally superimposing the signals from different users/antennas/relay nodes. This property is very useful for multi-user, multi-antenna and ad hoc environments. For this reason, SCM has been frequently used as a theoretical concept in the derivation of the channel capacity in such environments.

However, inter-layer interference constitutes a major obstacle in practice for SCM. Theoretically, such interference can be resolved through successive interference cancelation (SIC) [9], [10], but SIC is effective only when ideal codes are involved and it may lead to considerable performance degradation when non-ideal codes are involved. For this reason, compared with other schemes such as trellis coded modulation (TCM) and bit-interleaved coded modulation (BICM), SCM has mostly remained as a theoretic concept in the past.

With the advent of turbo and low-density-parity-check (LDPC) codes, low-cost iterative detection techniques have been studied for SCM [3], [5], [8]. In particular, the layer-by-layer detector outlined in [3], [8] (based on the detector for interleave-division multiple-access (IDMA) [11]) has complexity O(K) per symbol for a K-layer SCM. As a comparison, the detection complexity is O(2K) per symbol for a TCM or BICM scheme defined over a 2K-ary constellation. Thus, SCM can offer an attractive performance-complexity tradeoff, especially for very high-rate applications.

Most existing work on SCM so far relies on Monte Carlo simulations for performance evaluation. In this paper, we will conduct a comprehensive performance analysis for SCM. We broadly classify SCM into two classes: single-code SCM (SC-SCM) and multi-code SCM (MC-SCM), as shown in Fig. 1. With SC-SCM, the bits in different layers are generated using a single encoder, which can be seen as a special BICM scheme [12], [13], [14] over the constellation formed by the superposition operation in (1). With MC-SCM, the bits in different layers belong to different codewords, which can be seen as a special multi-level coding (MLC) scheme [15], [16]. For simplicity, we will assume that the K encoders in Fig. 1(b) are all based on the same forward error control (FEC) code.

We will analyze both SC-SCM and MC-SCM using three different approaches based on, respectively, capacity, signal-to-noise-ratio (SNR) evolution, and error bounds. These approaches are useful in different aspects: capacity analysis establishes theoretical limits; evolution analysis is a convenient tool in fast assessing the performance of iterative receivers; and error bounds sketch the error floor behavior. We will compare SC-SCM and MC-SCM using these different approaches. We will show that MC-SCM and SC-SCM have different advantages when practical codes are concerned. For example, SC-SCM may have a relatively lower error floor, but MC-SCM may achieve a faster convergence speed. We will use various examples to demonstrate that the performance of SCM can be predicted using the analysis tools outlined in this paper with reasonable accuracy.

Section snippets

System model and capacity

This section examines the performance limits of SCM with different sub-optimal encoding/decoding strategies. We will compare SC-SCM and MC-SCM from the viewpoint of capacity. We will also analyze the performance loss with a sub-optimal SIC receiver using the tools developed in [17] for mismatched decoding problems.

Performance with iterative decoding

In this section, we will briefly outline the iterative receiver principles for SCM. We will then develop an SNR evolution technique to predict the performance of SCM receivers. Gaussian approximation is the key to the discussion in this section, which not only greatly reduces the operation complexity, but also greatly simplifies the analysis problem involved.

For MC-SCM over AWGN channels, the SNR evolution technique developed for IDMA [18] can be directly used. However, new treatments are

Error-rate analysis

Capacity analysis is important in establishing the performance limits. However, in many cases, error bounding analysis provides more insights into performance with practical codes. In this section, we outline some simple analytical methods to predict the asymptotic performance. We also discuss the factors that affect the error floor behavior using these methods.

Conclusions

We have presented a comprehensive study of two types of SCM schemes, namely, SC-SCM and MC-SCM. The basic features of SCM are reviewed. The information-theoretic analysis shows that MC-SCM outperforms SC-SCM in terms of capacity. It also shows that the performance loss caused by sub-optimal SIC decoding is not serious for SCM with proper power allocations. The evolution analysis and error bounds, respectively, can be used to characterize the iterative decoding convergence and error floor

Acknowledgement

The authors are grateful to Dr. Jinhong Yuan at The University of New South Wales for enlightening discussions.

Jun Tong received the B.E. degree in information engineering and the M.E. degree in signal and information processing from the University of Electronic Science and Technology of China, Chengdu, in 2001 and 2004, respectively, and the Ph.D. degree in electronic engineering from City University of Hong Kong, Hong Kong SAR in 2009. He is now with the School of Electrical Engineering and Computer Science, The University of Newcastle, NSW, Australia. His research interests are signal processing and

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  • Jun Tong received the B.E. degree in information engineering and the M.E. degree in signal and information processing from the University of Electronic Science and Technology of China, Chengdu, in 2001 and 2004, respectively, and the Ph.D. degree in electronic engineering from City University of Hong Kong, Hong Kong SAR in 2009. He is now with the School of Electrical Engineering and Computer Science, The University of Newcastle, NSW, Australia. His research interests are signal processing and coding techniques in communication systems.

    Li Ping received his Ph.D. degree at Glasgow University in 1990. He lectured at the Department of Electronic Engineering, Melbourne University, from 1990 to 1992, and worked as a member of research staff at Telecom Australia Research Laboratories from 1993 to 1995. He has been with the Department of Electronic Engineering, City University of Hong Kong, since January 1996, where he is now a chair professor. His research interests are communications systems and coding theory. Dr. Li Ping received a British Telecom-Royal Society Fellowship in 1986, the IEE J J Thomson premium in 1993 and a Croucher Foundation Award in 2005.

    This work was fully supported by a grant from the Research Grant Council of the Hong Kong SAR, China [Project No. CityU 117508].

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