# A History of Channel Coding in Aeronautical Mobile Telemetry and Deep-Space Telemetry
## 3 Deep-Space Telemetry
### In Search of the Missing 2 dB--Turbo Codes
The switch then moves to position B for 4 bits for trellis termination. Trellis termination refers to the state of the encoder at the end of transmission. The performance of the decoder (the _sequence_ estimator) is improved when the beginning state and the ending state of the encoder are known. For non-recursive encoders, trellis termination is straightforward: append zeros to the end of the information block to produce the all-zeros state in the encoder. For recursive encoders (the case here), the bits to be appended depend on the encoder state after the input of the \(k\)-th information bit. Divsalar-Pollara [81] showed that a feedback method can be used to terminate the encoder in the all-zeros state. The Divsalar-Pollara technique is the one used in the CCSDS standard. The first use of turbo codes in space was part of an experimental package on ESA's _Small Missions for Advanced Research in Technology_-1 (_SMART_-1) that was launched to the Moon in September 2003. An experimental instrument called KaTE (Ka-band transmission experiment) carried a CCSDS turbo encoder. The KaTE instrument transmitted rate-1/4 turbo-encoded frames that were successfully received at ESA's tracking site at Villafranca del Castillo, Spain, and decoded by a turbo decoder developed by Space Engineering Rome (Italy) and Politecnico of Torino, Italy on behalf of the European Space Agency [82; 83]. As an experiment, turbo-coded transmissions from _SMART_-1 were not used for a significant telemetry downlink [77]. The first mission to use CCSDS turbo codes in the main telemetry downlink was NASA's _Messenger_, the first Mercury orbiter, launched on August 2004 attaining Mercury orbit in March 2011. _Messenger_ used the CCSDS rate-1/6 turbo code with \(k=8920\) to encode telemetry at a variety of rates up to 104 kbits/second [82]. The main telemetry downlink was in the 8.4 GHz band [84] using the first phased array antenna deployed in space [85; 86]. ESA's _Rosetta_ spacecraft was launched in March 2004 and attained orbit around the comet 67P/Churyumov-Gerasimenko in August 2014. _Rosetta_ was the first spacecraft to _orbit_ a comet. A lander called _Philae_ detached from the orbiter _Rosetta_ and performed the first successful landing on a comet in November 2014. The _Rosetta_-to-Earth telemetry link operated at 5-20 kbits/s, depending on the distance [87]. The original plan was to use the NASA/CCSDS standard concatenated code \begin{table}
\begin{tabular}{c l} \hline \hline
**Turbo Code Rate** & **Turbo Code Outputs** \\ \hline
1/2 & out 0a, out 1a, out 0a, out 1b, \(\dots\), repeated \((k+4)/2\) times \\
1/3 & out 0a, out 1a, out 1b, \(\dots\), repeated \(k+4\) times \\
1/4 & out 0a, out 2a, out 3a, out 1b, \(\dots\), repeated \(k+4\) times \\
1/6 & out 0a, out 1a, out 2a, out 3a, out 1b, out 3b, \(\dots\), repeated \(k+4\) times \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The relationship between the turbo code rate and the constituent code output connections. Adapted from [50]. Figure 17: The CCSDS turbo code encoder: (**a**) The turbo code structure based on two identical rate-1/4 systematic convolutional encoders and an information block buffer that also serves as an interleaver; (**b**) A block diagram of the constituent rate-1/4 systematic convolutional encoder. comprising the (7,1/2) convolutional code as the inner code, an interleaver, and the (255,233) Reed-Solomon code as the outer code. The CSSD's turbo encoder was programmed into the software chain feeding the PM modulator [79]. When the CCSDS turbo code was used, the concatenated code was bypassed. The _Philae-Rosetta_ RF telemetry link operated at 2033.2 MHz using QPSK with the square-root raised-cosine pulse shape [88]. The data rate was 16.384 kbits/s. The CCSDS standard (7,1/2) convolutional code was used on the link. Soft-decision decoding using the Viterbi algorithm was performed on _Rosetta_. The experiments using the CCSDS turbo codes were so successful that CSSD's turbo codes have been used in most subsequent missions by both NASA and ESA [89].