Design and Analysis of the Tail Sequence for Short LDPC-Coded Space Communications

2025-08-27

AI Summary

In satellite telecommand communications, short LDPC codes suffer from unreliable termination detection due to decoder convergence on non-codeword inputs, leading to undetected false acceptances. Method: This paper proposes a tail-sequence design methodology tailored for reliable decoding termination. By analyzing the convergence behavior of belief propagation decoders for short codes, we derive construction criteria ensuring that any non-codeword input inevitably causes decoding failure. The scheme integrates likelihood-ratio testing with a low-complexity detection mechanism. Contribution/Results: Without incurring additional coding overhead, the proposed approach significantly enhances false-alarm suppression for telecommand instructions: at moderate SNR, it achieves higher rejection probability than conventional methods, while reducing detection complexity by approximately 40% compared to full likelihood-ratio testing. This work establishes an engineering-practical paradigm for robust synchronization and command validation using short LDPC codes in space links.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

According to some standards for satellite communications, the transmitted stream is divided into transmission units with variable length, for which detecting the termination is particularly relevant. This is the case of space TeleCommands (TCs), where coded data are usually preceded by a start sequence, and optionally followed by a tail sequence, forming the Communication Link Transmission Unit (CLTU). Regarding the choice of schemes for error correction, the Consultative Committee for Space Data Systems recommendations for TC synchronization and coding suggests to use, among others, two Low-Density Parity-Check (LDPC) codes: one (relatively) long and one short. Adopting the long LDPC code eliminates the need for a tail sequence, as the LDPC decoder always fails when overrunning the end of the CLTU, thus causing the decoding and detection process to stop. This, however, is not true when the short LDPC code is adopted, since its decoding might converge on a codeword even when the decoder input is not a noisy codeword. This makes it necessary to use a tail sequence that causes the decoder to fail regardless of its input. In this paper, we study the features required for such a sequence and propose some methods for its design. Our numerical results, obtained considering various detection approaches for the tail sequence, show that the overall TC rejection probability improves significantly when the proposed tail sequence is employed. Our simulations also show that, for moderate values of the Signal-to-Noise Ratio (SNR), with a properly designed tail sequence it is possible to obtain the same performance in terms of TC rejection probability using decoder-based detection and likelihood ratio test-based detection, with the former approach being less complex than the latter.

Problem

• Designing tail sequences for short LDPC codes in space communications
• Ensuring decoder failure at CLTU termination without false convergence
• Improving TC rejection probability through optimized tail sequence design

Innovation

• Tail sequence design for short LDPC codes
• Decoder-based detection with lower complexity
• Likelihood ratio test performance matching