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

## TL;DR

This paper proposes a novel tail sequence design for short LDPC codes in space communications, improving transmission unit detection and rejection probability while reducing detection complexity.

## Contribution

It introduces specific features and methods for designing tail sequences that enhance detection performance for short LDPC-coded space communication links.

## Key findings

- Significant increase in TC rejection probability with the proposed tail sequence
- Comparable performance of decoder-based detection and likelihood ratio test at moderate SNR
- Reduced complexity in detection approach using the tail sequence design

## 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.

---
Source: https://tomesphere.com/paper/2508.19858