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Lattice-Based Analog Mappings for Low-Latency Wireless Sensor Networks

Pedro Suárez-Casal, Óscar Fresnedo, Darian Pérez-Adán, Luis Castedo

TL;DR

This paper tackles low-latency transmission of spatially correlated analog data from multiple sensors over fading SIMO MACs by proposing lattice-based analog JSCC. It develops a multidimensional encoding using Craig's lattices and an MMSE decoder augmented with sphere decoding and MAP estimation to exploit both lattice structure and source correlation. The authors derive practical encoding strategies (including an alternative Craig's lattice construction) and a parameter optimization loop that balances lattice density, decoding ambiguity, and power constraints. Simulation results show that lattice-based analog JSCC can achieve meaningful reliability gains over zero-delay mappings and approach separation-based bounds at small block sizes, making it a viable alternative for URLLC in WSN/IoT scenarios. The approach offers flexible trade-offs between codeword size, latency, and computational load, with Craig's lattices providing an attractive balance between performance and complexity.

Abstract

We consider the transmission of spatially correlated analog information in a wireless sensor network (WSN) through fading single-input and multiple-output (SIMO) multiple access channels (MACs) with low-latency requirements. A lattice-based analog joint source-channel coding (JSCC) approach is considered where vectors of consecutive source symbols are encoded at each sensor using an n-dimensional lattice and then transmitted to a multiantenna central node. We derive a minimum mean square error (MMSE) decoder that accounts for both the multidimensional structure of the encoding lattices and the spatial correlation. In addition, a sphere decoder is considered to simplify the required searches over the multidimensional lattices. Different lattice-based mappings are approached and the impact of their size and density on performance and latency is analyzed. Results show that, while meeting low-latency constraints, lattice-based analog JSCC provides performance gains and higher reliability with respect to the state-of-the-art JSCC schemes.

Lattice-Based Analog Mappings for Low-Latency Wireless Sensor Networks

TL;DR

This paper tackles low-latency transmission of spatially correlated analog data from multiple sensors over fading SIMO MACs by proposing lattice-based analog JSCC. It develops a multidimensional encoding using Craig's lattices and an MMSE decoder augmented with sphere decoding and MAP estimation to exploit both lattice structure and source correlation. The authors derive practical encoding strategies (including an alternative Craig's lattice construction) and a parameter optimization loop that balances lattice density, decoding ambiguity, and power constraints. Simulation results show that lattice-based analog JSCC can achieve meaningful reliability gains over zero-delay mappings and approach separation-based bounds at small block sizes, making it a viable alternative for URLLC in WSN/IoT scenarios. The approach offers flexible trade-offs between codeword size, latency, and computational load, with Craig's lattices providing an attractive balance between performance and complexity.

Abstract

We consider the transmission of spatially correlated analog information in a wireless sensor network (WSN) through fading single-input and multiple-output (SIMO) multiple access channels (MACs) with low-latency requirements. A lattice-based analog joint source-channel coding (JSCC) approach is considered where vectors of consecutive source symbols are encoded at each sensor using an n-dimensional lattice and then transmitted to a multiantenna central node. We derive a minimum mean square error (MMSE) decoder that accounts for both the multidimensional structure of the encoding lattices and the spatial correlation. In addition, a sphere decoder is considered to simplify the required searches over the multidimensional lattices. Different lattice-based mappings are approached and the impact of their size and density on performance and latency is analyzed. Results show that, while meeting low-latency constraints, lattice-based analog JSCC provides performance gains and higher reliability with respect to the state-of-the-art JSCC schemes.
Paper Structure (25 sections, 1 theorem, 45 equations, 12 figures, 4 tables)

This paper contains 25 sections, 1 theorem, 45 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Organization
  3. Notation
  4. Fundamentals of Lattices
  5. Sphere Packing
  6. Lattice-Based Quantization
  7. System Model
  8. Real-Valued Equivalent Model
  9. Multi-Dimensional Lattice-Based Analog JSCC
  10. Craig's Lattices
  11. Standard Construction
  12. Alternative Construction
  13. Craig's Lattice Parameters
  14. MMSE Decoding
  15. Sphere Decoding with MAP Estimation
  16. ...and 10 more sections

Key Result

Lemma 4.1

Given the cyclotomic ring of integers $\mathbb{Z}[\zeta_p]$ with $p$ prime, the ideal $G=(T_1(\zeta_p) \cdot \ldots \cdot T_m(\zeta_p))\subset \mathbb{Z}[\zeta_p]$, generated by the product of $m$ polynomials in the form $T_i(\zeta_p)=\zeta_p^{k_i}-1, k_i\ge 1$, is equal to the ideal $I=((1-\zeta_p)

Figures (12)

  • Figure 1: Circle packing problem and deep holes.
  • Figure 2: Block diagram of the considered analog JSCC communication system.
  • Figure 3: Example of the partition of the source space using bi-dimensional truncated Gaussian variables.
  • Figure 4: SDR (dB) for different sizes of a Craig's lattice-based mapping ($n \in \lbrace 16, 36, 52 \rbrace$) with $m=3$ for $n=16$, $m=5$ for $n=36$ and $m=3$ for $n=52$, respectively, and for the $(\text{BW}_{16})$ lattice in a $4\times20$WSN SIMO MAC setup with $\rho=0.95$.
  • Figure 5: SDR (dB) obtained with $m\in \lbrace2,3,4,5\rbrace$ by considering a Craig's lattice-based mapping (with size $n=36$) in a $4\times 20$WSN SIMO MAC setup with spatial correlation $\rho=0.95$.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Lemma 4.1
  • proof