Telecommand Rejection Probability in CCSDS-Compliant LDPC-Coded Space Transmissions with Tail Sequence

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. A low-complexity approach classically used to detect CLTU termination is to choose a non-correctable string as the tail sequence, and then exploit the decoder failure on that sequence as termination detection. This works very well with the BCH code, for which bounded-distance decoders are employed. Instead, when the same approach is employed with LDPC codes and probabilistic belief propagation iterative decoders, the scenario becomes more challenging. In this paper, we study CCSDS-compliant space communications in which LDPC codes are employed, and analyze the TC rejection probability both theoretically and through intensive numerical simulations. Such a performance figure, being the rate at which CLTUs are discarded, should clearly be minimized. Our numerical analysis considers many different choices of the system parameters (e.g., length of the CLTU, decoding algorithm, maximum number of decoding iterations). Particular attention is devoted to the probability of not-acknowledged termination, i.e., the probability that the tail sequence is not recognized.