130x1g2 - CCSDS

TM SYNCHRONIZATION AND CHANNEL CODING—SUMMARY OF CONCEPT AND RATIONALEachieves approximately the same undetected error rate for any of the recommended telemetrychannel codes.A much lower undetected error rate is achieved when the RS code with E = 16 is used, eitherby itself or concatenated with an inner convolutional code. In this case, the undetected errorrate of the RS decoder is on the order of 1/E! ≈ 5·10 -14 , which is many orders of magnitudebetter than the validation offered by the CRC code. Thus the error detection capability of theCRC code is superfluous when the RS code with E = 16 is used.The RS code with E = 8 offers much lower error detection capability, on the same order asthat provided by the 16-bit CRC code. Similarly, a Turbo decoder equipped with a smartstopping rule that notes whether the decoder’s iterations converge to a valid codeword canachieve some degree of error detectability and somewhat alleviate the need for the 16-bitCRC code. However, in these borderline cases the CRC code is still required. It is alsorequired for uncoded data or convolutionally coded data, which offer absolutely no capabilityfor error detection on their own.If a lower detected error rate is desired than that offered by the recommended 16-bit CRCcode, and RS coding is not used, then one option is to use a 32-bit or 48-bit CRC code (not inthe CCSDS Recommended Standards).9.5 CODE TRANSPARENCYRotationally invariant (transparent) coding schemes are used to overcome the phaseambiguity inherent in usual coherent demodulation techniques. For the transmission over aband-limited channel using phase-coherent demodulation, to estimate the carrier phase, thereceiver uses its knowledge of the signal set S, which is the set of points produced by themodulator. By examining the pattern of received signal points, the receiver can infer thecarrier phase up to an ambiguity corresponding to a rotational symmetry of S.A counterclockwise rotation of x degrees about the origin is denoted by ρ. A rotationalsymmetry of the signal set S is a rotation ρ mapping S into itself. The set of all the rotationalsymmetries of S is called the rotational symmetry group . If has n elements then it is acyclic group generated by the rotation ρ of x = 360/n degrees (the smallest non-zero rotationbelonging to it).As an example, an M-PSK constellation has M rotational symmetries. In particular, a 2-PSKconstellation has 2 rotational symmetries: = {ρ 0,ρ 1}, while a 4-PSK constellation has 4rotational symmetries = {ρ 0,ρ 1,ρ 2,ρ 3}, as a square QAM constellation (16-QAM, 64-QAM,256-QAM), where ρ i= 90*i. For non-square QAM constellations, depends on the signalchoice.When used in a modulation scheme with coherent demodulation, the carrier phase isestimated from the ensemble of the received signal points. However, an ambiguitycorresponding to a rotation of cannot be solved without external reference. For example, ifCCSDS 130.1-G-2 Page 9-21 November 2012