Near-Optimal Nonbinary Index Assignment for Equiprobable Lattice Quantizers

Abstract

Index assignment (IA) is a low-complexity joint source-channel coding technique that has the potential for use in low-latency and low-power applications, such as wireless sensor networks (WSNs). Though binary IA has been extensively studied for assigning binary indices to quantized codewords (or symbols) under the assumption of binary symmetric channels (BSCs), real-world scenarios often use $M$ -ary modulations. Directly applying binary IAs designed for BSCs to $M$ -ary modulations results in suboptimal performance. In this paper, we investigate the $M$ -ary IA, which assigns $M$ -ary labels to quantized codewords (or symbols), assuming the use of a equiprobable lattice quantizer. For such a system, we derive a tight performance bound and propose a near-optimal IA scheme based on a two-step design. In addition, we propose explicit IA constructions for practical modulation schemes, including PAM, QAM, and PSK. Our proposed IA design is rigorously proven to be optimal for 3-PSK and QPSK, whereas for larger modulation orders, the proposed IA constructions approach the bounds within small gaps. Our simulations show that the constructed IA scheme can achieve significant energy savings compared to the conventional binary IA scheme. Specifically, in some WSN scenarios, the proposed IA for 16-QAM is shown to achieve significant reductions in energy consumption relative to the conventional binary counterpart.

Keywords

• Discrete memoryless channel
• index assignment
• joint source-channel coding
• quantization