# A History of Channel Coding in Aeronautical Mobile Telemetry and Deep-Space Telemetry
## 4 Aeronautical Mobile Telemetry
### Channel Coding in the 21 st Century  
The first serious test of channel coding with error correction capabilities in a realistic aeronautical mobile telemetry environment was described by [PERSON] [14]. In the tests, a provision was made to store data on the test article. The same data were transmitted to the ground station and the data bit decisions were recorded on the ground. Error patterns were generated by comparing the two. The datasets used to generate the error patterns were derived from tests involving the T-39 Sabreliner [178] at Edwards AFB, the F/A-18 Hornet [179] at NAS Patuxent River, and the V-22 Osprey [162] also at NAS Patuxent River [14]. As a result, the error patterns captured the realities of the aeronautical mobile telemetry channel: a combination of random errors and burst errors, the latter due to signal dropouts caused by difficult propagation scenarios. The experiment tested the performance of an interleaver followed by a \((255,k)\) Reed-Solomon code for \(k=224\), 207, 199, and 146. The test results were mixed. The coding technique performed well as long as the deinterleaved error bursts did not overwhelm the error-correcting capability of the code. Error bursts lasting longer than 500 ms were a problem. Unfortunately, many of the dropouts were 500 ms or more. The findings were consistent with earlier simulations using length-255 Reed-Solomon codes reported in [148] based on error sequences derived from F-16 flight data described in [147; 180]. Turbo codes were introduced by [PERSON] et al, in 1993 [76]. The original code was based on a parallel concatenation of recursive convolutional codes. Convolutional codes work well for low-rate coding applications. In aeronautical mobile telemetry, where severe bandwidth constraints are dominant, the bandwidth expansion associated with low-rate codes renders them impractical. Motivated by the trend that block codes tend to perform better for high-rate coding applications, Pyndiah introduced turbo product codes in 1994 [181]. By 2002, at least one single-chip solution was available on the commercial market [182]. A product code is based on the \"product\" of an \((n_{1},k_{1})\) linear systematic block code and an \((n_{2},k_{2})\) linear systematic block code. The resulting code is usually denoted as an \((n_{1},k_{1})\times(n_{2},k_{2})\) code. A graphical representation of the encoder is shown in Figure 22 [181]. A block of \(k_{1}\times k_{2}\) information bits is read into a \(k_{1}\times k_{2}\) array. The \((n_{2},k_{2})\) code is applied to each row of the block to produce an intermediate block of \(k_{1}\times n_{2}\)bits. The \((n_{1},k_{1})\) code is applied to each column of the intermediate block to produce an \(n_{1}\times n_{2}\) block of coded bits. The bits are read out in a predefined fashion (e.g., row-by-row, column-by-column, or along diagonals) and used to modulate an RF carrier. The code rate of the product code is \(k_{1}k_{2}/(n_{1}n_{2})\). At the decoder, soft information from the demodulator is organized into an \(n_{1}\times n_{2}\) matrix corresponding to that in Figure 22. Soft decision decoding alternates between the rows and columns in an iterative fashion using the turbo principle [181]. Laboratory experiments using PCM/FM and SOQPSK-TG are described in [183]. Soft output information for PCM/FM was derived from the trellis detector. Soft output information for SOQPSK-TG was derived from the detection filter outputs. (See [184] for a description of the SOQPSK-TG symbol-by-symbol detector and its application to soft-decision decoding). The experiment evaluated the highest rate codes produced by the AHA4540 encoder/decoder chip: the \((32,26)\times(32,26)\), \((64,57)\times(64,57)\), and \((128,120)\times(128,120)\) product codes. The measured coding gains were 3.0-3.5 dB for PCM/FM and 6 dB for SOQPSK-TG. (Note that the coding gain for turbo-product coded PCM/FM with trellis detection relative to uncoded PCM/FM with limiter/discriminator detection is 3 dB better: 6-6.5 dB).