communications systems and var- ious standards. For example, the 3G standards use two convolution (2,1,9) and (3,1,9) codes, shown in Figure 6.18. The 4G standards of mobile communications also specify a slightly different class of convolutional codes. Error Control Coding Accumulated branch metric = 4 Accumulated branch metric = 0 Figure 6.16 Branch metric calculation 1.0E + 00 1.0E - 01 1.0E - 02 1.0E-03 No coding 1.0E-04 coding 1.0E-05 Eb/No (dB) Figure 6.17 BER for a convolutional (2,1,3) code Input bit Output bit 1 Output bit 2 Input bit Output bit 1 Output bit 2 Output bit 3 Figure 6.18 Convolutional (2,1,9) and (3,1,9) codes used in the 3G standards Broadband Telecommunications Technologies and Management Case Study 6.2 The first application for error control codes was in the NASA's Mariner probes (pictured)3 in the early 1960s specifically for transmission of data collected by their sensors. In particular, Mariner 4 which flew by Mars in 1964 had cameras to take photos of the surface of the planet. Due to the large size of the photos and the low SNR at the Earth's receiver, the most accurate (and perhaps the only practical) way of transmitting these photos back was to convert them into a digital stream and transmit them digitally. The channel capacity however was small, and therefore photos were converted to digital and stored locally on a digital tape which had a capacity of 20 photos. These photos were then transmitted to Earth as a digital file with a certain block size. Error control coding techniques, including CRC and FEC were used to ensure these pic- tures were received error-free. For example Mariner 9 used a (32,6) block code. Such transmission would have been impossible considering the large path loss and the small transmission power on-board the probe. Furthermore, the FEC coding technique ensured that BLER remained small, resulting in fewer retransmissions to recover erroneous data blocks. Space communications have since relied on digital communications to ensure information collected by spac