Wireless Communications

11Turbo Codes and Turbo Principle

Abstract

Turbo codes are a powerful means to approach the capacity of an AWGN channel. A well-performed turbo code is usually synthesized by using two simple encoders, in serial or parallel concatenation, so that an iterative algorithm can be used for efficient decoding. A basic philosophy of turbo codes is, therefore, to create a two-device mechanism and derive an information-exchange algorithm to optimally retrieve the original message sequence. The two devices can be a pair of constituent encoders or a combination of an encoder and any other structure in a communication system. This widely applicable philosophy is known as the turbo principle. It is shown that turbo codes can effectively approach the AWGN channel capacity, leaving a gap of only dB from the Shannon bound at the bit-error rate of . The turbo principle is also widely used in turbo equalization and turbo CDMA.

11.1 Introduction and philosophical discussion

The maximum bit rate for error-free transmission over a noisy channel is upper-bounded by its channel capacity. In his seminal paper, Shannon [1] demonstrated that the channel capacity could be theoretically approached by using an infinitely long random code. In practical applications, however, pure random codes are difficult ...