Convolutional Codes: Construction and Encoding

This chapter introduces a widely used class of codes, called convolutional codes, which are used in a variety of systems including today’s popular wireless standards (such as 802.11) and in satellite communications. They are also used as a building block in more powerful modern codes, such as turbo codes, which are used in wide-area cellular wireless network standards such as 3G, LTE, and 4G. Convolutional codes are beautiful because they are intuitive, one can understand them in many different ways, and there is a way to decode them so as to recover the most likely message from among the set of all possible transmitted messages. This chapter discusses the encoding of convolutional codes; the next one discusses how to decode convolutional codes efficiently. Like the block codes discussed in the previous chapter, convolutional codes involve the computation of parity bits from message bits and their transmission, and they are also linear codes. Unlike block codes in systematic form, however, the sender does not send the message bits followed by (or interspersed with) the parity bits; in a convolutional code, the sender sends only the parity bits. These codes were invented by Peter Elias ’44, an MIT EECS faculty member, in the mid-1950s. For several years, it was not known just how powerful these codes are and how best to decode them. The answers to these questions started emerging in the 1960s, with the work of people like Andrew Viterbi ’57, G. David Forney (SM ’65, Sc.D. ’67, and MIT EECS faculty member), Jim Omura SB ’63, and many others.