Hadamard transform can be used to decompose any signal into its constituent Hadamard components. In this sense it works just like a Fourier transform but with the components based on sequency rather than frequency. As with the Fourier transform, a number of these components can be discarded without destroying the original data SO the Hadamard transform can be used for compression. The Hadamard transform can also be used for error correction. A much-quoted example is the use of Hadamard transforms to code the pictures coming back from the visits to the moon in the 1960s and the Mariner and Voyager missions to Mars. The pictures were produced by taking three black and white pictures in turn through red, green and blue filters. Each picture was considered as a thousand by thousand matrix of black and white pixels and graded on a scale of 1-16 according to its greyness (white is 1, black is 16). These grades were then used to choose a codeword in an eight error correction code based on a Hadamard matrix of order 32. The codeword was transmitted to earth and then error corrected. It was this practical experience with applied Hadamard transforms that led on to the use of Hadamard transforms in present-generation cellular systems including GSM and CDMA. These use convolutional and block coding to increase the distance between a 0 and a 1 or rather a and a +1. The process is described in more detail below. Note that channel coding is a distinct and separate though related process to code division multiple access. Both processes exploit the properties of the Hadamard matrix. Channel coding produces 'coding gain' and code division multiple access produces 'spread- ing gain'. Coding gain can be of the order of 10 dB or SO and spreading gain in the order of 20 dB for lower user data rates. Together they show the extent to which the Hadamard transform contributes to the link budget of legacy cellular radio systems. OFDMA systems have to improve on this benchmark on all performance metrics not purely on single per user peak da