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Parallel Coding for Orthogonal Delay-Doppler Division Multiplexing

Qi Li, Jinhong Yuan, Min Qiu

TL;DR

This work addresses Doppler-induced challenges in 2D delay-Doppler modulation by introducing a parallel channel encoding (PCE) scheme for ODDM and an iterative, tightly-coupled detection/decoding framework with successive decoding feedback (SDF). By encoding each delay-Doppler row with independent short codewords, the receiver exchanges soft information with the detector on a per-row basis, enabling faster convergence and reduced complexity compared to a conventional single long-codeword approach. The authors develop soft interference cancellation based SIC-MMSE detection, perform density evolution and finite-blocklength analyses, and demonstrate via simulations that PCE-SDF outperforms SCE-PDF by up to about 1 dB with significantly lower complexity. The proposed approach offers a practical path to higher reliability in high-mobility channels and can be extended to CP-ODDM, highlighting the benefits of joint detector-decoder design in DD-domain modulations.

Abstract

This paper proposes a novel parallel coding transmission strategy and an iterative detection and decoding receiver signal processing technique for orthogonal delay-Doppler division multiplexing (ODDM) modulation. Specifically, the proposed approach employs a parallel channel encoding (PCE) scheme that consists of multiple short-length codewords for each delay-Doppler multicarrier (DDMC) symbol. Building upon such a PCE transmission framework, we then introduce an iterative detection and decoding algorithm incorporating a successive decoding feedback (SDF) technique, which enables instant information exchange between the detector and decoder for each DDMC symbol. To characterize the error performance of the proposed scheme, we perform density evolution analysis considering the finite blocklength effects. Our analysis results, coupled with extensive simulations, demonstrate that the proposed PCE scheme with the SDF algorithm not only showcases a better overall performance but also requires much less decoding complexity to implement, compared to the conventional benchmark scheme that relies on a single long channel code for coding the entire ODDM frame.

Parallel Coding for Orthogonal Delay-Doppler Division Multiplexing

TL;DR

This work addresses Doppler-induced challenges in 2D delay-Doppler modulation by introducing a parallel channel encoding (PCE) scheme for ODDM and an iterative, tightly-coupled detection/decoding framework with successive decoding feedback (SDF). By encoding each delay-Doppler row with independent short codewords, the receiver exchanges soft information with the detector on a per-row basis, enabling faster convergence and reduced complexity compared to a conventional single long-codeword approach. The authors develop soft interference cancellation based SIC-MMSE detection, perform density evolution and finite-blocklength analyses, and demonstrate via simulations that PCE-SDF outperforms SCE-PDF by up to about 1 dB with significantly lower complexity. The proposed approach offers a practical path to higher reliability in high-mobility channels and can be extended to CP-ODDM, highlighting the benefits of joint detector-decoder design in DD-domain modulations.

Abstract

This paper proposes a novel parallel coding transmission strategy and an iterative detection and decoding receiver signal processing technique for orthogonal delay-Doppler division multiplexing (ODDM) modulation. Specifically, the proposed approach employs a parallel channel encoding (PCE) scheme that consists of multiple short-length codewords for each delay-Doppler multicarrier (DDMC) symbol. Building upon such a PCE transmission framework, we then introduce an iterative detection and decoding algorithm incorporating a successive decoding feedback (SDF) technique, which enables instant information exchange between the detector and decoder for each DDMC symbol. To characterize the error performance of the proposed scheme, we perform density evolution analysis considering the finite blocklength effects. Our analysis results, coupled with extensive simulations, demonstrate that the proposed PCE scheme with the SDF algorithm not only showcases a better overall performance but also requires much less decoding complexity to implement, compared to the conventional benchmark scheme that relies on a single long channel code for coding the entire ODDM frame.

Paper Structure

This paper contains 13 sections, 27 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. ODDM System Model
  3. Proposed Coding Scheme for ODDM
  4. SCE Scheme for ODDM
  5. Iterative SIC-MMSE Detection for ZP-ODDM
  6. Parallel Encoding for ODDM
  7. Joint Detection and Decoding for Parallel Encoded ODDM
  8. Performance Analysis
  9. SCE-PDF Analysis
  10. PCE-SDF Analysis
  11. Complexity Analysis
  12. Simulations
  13. Conclusion

Figures (12)

  • Figure 1: Time domain input-output relation for the $n$-th block with $L$ = 3
  • Figure 2: Single Codeword Encoding (SCE) for ZP-ODDM
  • Figure 3: Parrallel Channel Encoding (PCE) for ZP-ODDM
  • Figure 4: Successive decoding feedback (SDF) joint detection and decoding receiver for ZP-ODDM ($M=5$)
  • Figure 5: Joint detection and decoding for each codeword
  • ...and 7 more figures

Theorems & Definitions (1)

  • Remark 1