# A History of Channel Coding in Aeronautical Mobile Telemetry and Deep-Space Telemetry
## 3 Deep-Space Telemetry
### Mariner  
The _Mariner_ program was one of the first efforts to send unmanned spacecraft to other planets. _Mariner_ launched ten spacecraft (eight of which were successful) between 1962 and 1973 [25]. _Mariner_ 2 and 5 explored Venus, _Mariner_ 3, 4, 6, 7, and 9 explored Mars, and _Mariner_ 10 explored both Venus and Mercury [25]. The telemetry link on _Mariner_s 1-5 used uncoded PCM/PSK/PM [26]. _Mariner_ 6, 7, and 9, launched 1969-1971 used channel coding [27; 28]. Figure 6: The rate-\(1/2\) convolutional encoders used by the _Pioneer_ program are as follows: (**a**) The systematic rate-\(1/2\) convolutional encoder for _Pioneer_ 9; (**b**) The non-systematic rate-\(1/2\) convolutional encoder for _Pioneer_ 10 and 11. The box with the “D” is a one-bit delay register. A block diagram representing the telemetry subsystem on the _Mariner_ 6 spacecraft is shown in Figure 7. The telemetry link comprised two subcarriers, each modulated using PCM/PSK. The subcarriers were combined, and the resulting combination phase-modulated an S-band carrier at 2295 MHz. The low-rate subcarrier carried the engineering data: time-division multiplexed binary words representing samples of transducer outputs [26]. During the cruise phase, uncoded engineering data were transmitted on the subcarrier at either 33 1/3 bits/s or 8 1/3 bits/s [27]. During image transmission, uncoded engineering data were transmitted to the subcarrier at either 66 2/3 bits/s or 270 bits/s. The high-rate subcarrier transmitted digitized images of Mars read back from tape storage. To capture the images, _Mariner_ 6 was equipped with a TV camera whose (continuous-time) output was recorded to magnetic tape using an onboard tape recorder. After an imaging session, the analog tape was played back at a lower speed through an A/D converter. The A/D converter output was recorded on a second onboard tape recorder. The digital data comprised 6-bit samples representing the grayscale level (64 grayscale levels) for each pixel in the digitized image. The data stored on the digital tape recorder was played back at an even lower speed for coding and transmission [27]. The (32,6) bi-orthogonal Reed-Muller code was used to protect pixel values. The bit rate was 16.2 kbits/s [27]. The encoder is described by the 6 \(\times\) 32 generator matrix [27]. \[\mathbf{G}= \begin{bmatrix}111111111111111111111111111111111111\\ 00000000000000011111111111111111111111\\ 000000000000001111111111111111111111111111111111\\ 0000000001111111111100000000011111111111111111111\\ 00001011110001111000011110000111110001111\\ 001101010101101010101010101101010110011\\ 01010101010101010101010101010101010101101\\ \end{bmatrix} . \tag{3}\]  
The code word \(\mathbf{c}=[c_{0}\ldots,c_{31}]\) corresponding to the data word \(\mathbf{b}=[b_{0},\ldots,b_{5}]\) may be computed using vector/matrix multiplication \(\mathbf{c}=\mathbf{bG}\) where all arithmetic operations are performed in GF(2). The circuit used on _Mariner_ to generate a codeword was different [27]. The Reed-Muller code was chosen because a computationally efficient decoding algorithm was available. The code comprises 64 length-32 codewords. The codewords can be viewed as a set of 32 orthogonal length-32 binary vectors together with their complements. For this reason, the (32,6) Reed-Muller code is sometimes called a \"bi-orthogonal\" code. Soft-decision decoding was performed using a correlator based on the Hadamard transform [29]. The coding gain for the _Mariner_ 6 and 7 configurations was 2.2 dB [27]. The last _Mariner_ mission, _Mariner_ 9, carried an infrared interferometer spectrometer (IRIS) experiment to provide information about the Martian atmosphere. Each measurement, called an interferogram, was sampled using 6-bit quantization to produce 4096 6-bit words. The middle 512 words of the interferogram contained essentially all of the interferogram information and required an equivalent bit error probability no more than \(10^{-5}\).