Optical Networks: A Practical Perspective - Part 31. This book describes a revolution within a revolution, the opening up of the capacity of the now-familiar optical fiber to carry more messages, handle a wider variety of transmission types, and provide improved reliabilities and ease of use. In many places where fiber has been installed simply as a better form of copper, even the gigabit capacities that result have not proved adequate to keep up with the demand. The inborn human voracity for more and more bandwidth, plus the growing realization that there are other flexibilities to be had by imaginative use of the fiber, have led people. | 270 Modulation and Demodulation power . In this sense the repetition code is useless since it has a negative coding gain. However codes with substantial coding gains that is which decrease the BER substantially for the same transmit power as in the uncoded system have been designed by mathematicians and communication engineers over the last 50 years. In the next section we discuss a popular and powerful family of such codes called Reed-Solomon codes. Reed-Solomon Codes A Reed-Solomon code named after its inventors Irving Reed and Gus Solomon does not operate on bits but on groups of bits which we will call symbols. For example a symbol could represent a group of 4 bits or a group of 8 bits a byte . A transmitter using a Reed-Solomon code considers k data symbols and calculates r additional symbols with redundant information based on a mathematical formula the code. The transmitter sends the n k r symbols to the receiver. If the transmitted power is kept constant since k r symbols have to be transmitted in the same duration as k symbols each symbol in the coded system has k k r the duration and hence k k r the energy of a symbol in the uncoded system. The receiver considers a block of n k r symbols and knowing the code used by the transmitter it can correctly decode the k data bits even if up to r 2 of the k r symbols are in error. Reed-Solomon codes have the restriction that if a symbol consists of m bits the length of the code n 2m 1. Thus the code length n 255 if 8-bit bytes are used as symbols. The number of redundant bits r can take any even value. A popular Reed-Solomon code used in most recently deployed submarine systems has parameters n 255 and r 16 and hence k n r 239. In this case 16 redundant bytes are calculated for every block of 239 data bytes. The number of redundant bits added is less than 7 of the data bits and the code is capable of correcting up to 8 errored bytes in a block of 239 bytes. This code provides a coding gain of about 6 dB. With
