Editing Mariner 9 (section)

== Error-correction codes achievements ==
[[File:Hadamard-Code.svg|thumb|Matrix of the Hadamard code (32, 6, 16) for the Reed-Muller Code (1, 5) of the NASA space probe Mariner 9]]To control for errors in the reception of the [[grayscale]] image data sent by Mariner 9 (caused by a low [[signal-to-noise ratio]]), the data had to be encoded before transmission using a so-called [[forward error correction|forward error-correcting code]] (FEC). Without FEC, noise would have made up roughly a quarter of a received image, while the FEC encoded the data in a redundant way which allowed for the reconstruction of most of the sent image data at reception.

Since the flown hardware was constrained with regards to weight, power consumption, storage, and computing power, some considerations had to be put into choosing an FEC, and it was decided to use a [[Hadamard code]] for Mariner 9. Each image pixel was represented as a six-bit binary value, which had 64 possible grayscale levels. Because of limitations of the transmitter, the maximum useful data length was about 30 bits. Instead of using a [[repetition code]], a [32, 6, 16] Hadamard code was used, which is also a 1st-order [[Reed-Muller code]]. Errors of up to seven bits per each 32-bit word could be corrected using this scheme.<ref name=youtube1/><ref name=youtube2/> Compared to a five-repetition code, the error correcting properties of this Hadamard code were much better, yet its data rate was comparable. The efficient decoding [[algorithm]] was an important factor in the decision to use this code. The circuitry used was called the "Green Machine", which employed the [[fast Fourier transform]], increasing the decoding speed by a factor of three.<ref name=denver/>