Analog coding techniques for communication systems: performance analysis of bandwidth reduction and expansion schemes

Abstract

This thesis investigates analog coding techniques for bandwidth-constrained communication systems, focusing on both bandwidth reduction and expansion scenarios. For bandwidth reduction, we analyze Low-Density Generator Matrix (LDGM)-like analog codes decoded via iterative message-passing algorithms. Our findings demonstrate that higher code rates and increased matrix sparsity significantly improve performance, with LDGM-like codes approaching theoretical limits for linear coding at high SNRs. For bandwidth expansion, we develop and evaluate three decoding methods for 1:2 and 1:3 multi-stage quantization schemes: direct decoding, independent stage-wise refinement, and optimal joint estimation. Through optimization of quantization levels and energy allocation across channels, we show that all methods achieve SDR curves nearly parallel to the theoretical OPTA curve. The optimal decoding method consistently outperforms others, though stage-wise decoding offers an attractive balance between performance and computational complexity. Our results confirm that carefully designed analog coding systems can effectively approach theoretical performance limits while maintaining reasonable implementation complexity, providing valuable insights for designing communication systems under varying bandwidth constraints.