On the Error Detection Capability of Combined LDPC and CRC Codes for   Space Telecommand Transmissions
  We present a method for estimating the undetected error rate when a cyclic redundancy check (CRC) is performed on the output of the decoder of short low-density parity-check (LDPC) codes. This system is of interest for telecommand links, where new LDPC codes have been designed for updating the current standard. We show that these new LDPC codes combined with CRC are adequate for complying with the stringent requirements of this kind of transmissions in terms of error detection. 
Marco Baldi, Nicola Maturo, Giacomo Ricciutelli, Franco Chiaraluce
cs.IT math.IT