Telecommand Rejection Probability for CCSDS-compliant LDPC-Coded Transmissions with Tail Sequence

TL;DR

The paper addresses TC rejection probability in CCSDS-compliant LDPC transmissions by analyzing start-detection, decoding failures, and tail-sequence termination. It introduces randomized and de-randomized tail sequences and evaluates iterative LDPC decoders (LLR-SPA, MSA, NMSA) under varying CLTU lengths and iteration limits, deriving both theoretical expressions and Monte Carlo results. The key finding is that a de-randomized TS design substantially lowers the not-acknowledged termination probability and overall TC rejection, especially for short CLTUs and multiple codewords, by increasing the TS distance to valid codewords and reducing decoder bias toward certain codewords. The work provides actionable insights for CCSDS standards and suggests future TS design optimized for iterative decoders to further minimize TC rejection and enhance operational efficiency.

Abstract

According to the Consultative Committee for Space Data Systems (CCSDS) recommendation for TeleCommand (TC) synchronization and coding, the Communications Link Transmission Unit (CLTU) consists of a start sequence, followed by coded data, and a tail sequence, which might be optional depending on the employed coding scheme. With regard to the latter, these transmissions traditionally use a modified Bose-Chaudhuri-Hocquenghem (BCH) code, to which two state-of-the-art Low-Density Parity-Check (LDPC) codes were later added. As a lightweight technique to detect the presence of the tail sequence, an approach based on decoding failure has traditionally been used, choosing a non-correctable string as the tail sequence. This works very well with the BCH code, for which bounded-distance decoders are employed. When the same approach is employed with LDPC codes, it is necessary to design the tail sequence as a non-correctable string for the case of iterative decoders based on belief propagation. Moreover, the tail sequence might be corrupted by noise, potentially converting it into a correctable pattern. It is therefore important that the tail sequence is chosen to be as much distant as possible, according to some metric, from any legitimate codeword. In this paper we study such problem, and analyze the TC rejection probability both theoretically and through simulations. Such a performance figure, being the rate at which the CLTU is discarded, should clearly be minimized. Our analysis is performed considering many different choices of the system parameters (e.g., length of the CLTU, decoding algorithm, maximum number of decoding iterations).

Figures (14)

• Figure 1: CLTU structure bluebook
• Figure 2: Communication System's Blocks Diagram when using LDPC codes
• Figure 3: Missed detection probability under hard correlation detection
• Figure 4: Comparison of TC rejection probability's leading components for different algorithms (randomized case)
• Figure 5: TC rejection probability for the three considered decoders (randomized case)