Turbo codes: Bounds and applications

This dissertation presents research conducted in the field of information theory. More specifically the results contained herein are related to channel coding and a class of high performance channel codes known as turbo codes.;Prior to the discovery of turbo codes, all known error control systems had to operate many decibels above the Shannon Limit to obtain reasonable error rates. In fact, no codes had exceeded the R0 bound. Since the Shannon Limit is fundamentally dependent on allowing the block length of a code to increase without bound, the performance of turbo codes is bounded away from the Shannon Limit. However, turbo code performance is extremely close to the Shannon Limit, thus a tight performance bound that is a function of the block length would be extremely useful in analysis of turbo codes.;In practice, the block length or amount of memory used by an error control code must be finite. Turbo codes are usually implemented as block codes. A good lower bound on the probability of a bit error for binary block codes is presented here. The bound is a function of the block length and is directly applicable to turbo codes. Turbo codes perform extremely close to this bound for a given block length, thus implying that the small gap between the performance point of turbo codes and the Shannon Limit is due to the block length constraint, not to poor code performance.;The excellent performance that turbo codes exhibit with QPSK on an AWGN channel has lead many researcher to investigate their performance in other communications systems. For example researchers have studied the application of turbo codes to high order constellation such as QAM, satellite communications links, cellular phone systems, and digital video broadcasting. One channel that is ubiquitous in this computer-driven era is the magnetic recording channel. The most well-known occurrence of this channel is the hard disk drive. Research on the application of turbo codes to the magnetic recording channel is presented. A coding scheme that uses serial concatenated turbo codes for the magnetic recording channel and exhibits excellent performance is described.