It has often been demonstrated that conventional 4-state turbo codes do not perform well in either the waterfall or error-rate flare regions due to poor inherent convergence and distance properties, especially for highly-punctured codes. This paper shows that the opposite can be true when carefully chosen data and parity puncture masks are used with matching puncture-constrained dithered relative prime (DRP) interleavers. With an interleaver length of K=223(8-meg), it is shown that waterfalls within 0.1 dB of capacity are possible for code rates R≥2/3. Waterfall performance can also be traded for improved distance to achieve very low error-rate flares. With an interleaver length of K=214= 16384, R=8/9, and 50% data puncturing, a packet error rate of 10-6was achieved within 0.57 dB of the corresponding binary sphere packing bound without using a cleanup code.

Rate-compatible turbo codes are designed using dithered relative prime (DRP) interleavers with data puncturing. DRP interleavers are simple to implement and memory-efficient. Their repetitive structure facilitates finding interleaver parameters that provide excellent performance at both high and low error rates. With puncture-constrained DRP interleavers, the data and parity puncture patterns can be matched to the interleaver, thereby maintaining excellent performance for very high code rates. This makes them ideally suited to rate- compatible coding applications. Excellent waterfall and error-flare performance is demonstrated for rate-compatible turbo codes with code rates ranging from 1/3 to 8/9.

For decades, the de facto standard for forward error correction was a convolutional code decoded with the Viterbi algorithm, often concatenated with another code (e.g., a Reed-Solomon code). But since the introduction of turbo codes in 1993, much more powerful codes referred to collectively as turbo and turbo-like codes have eclipsed classical methods. These powerful error-correcting techniques achieve excellent error-rate performance that can closely approach Shannon's channel capacity limit. The lure of these large coding gains has resulted in their incorporation into a widening array of telecommunications standards and systems. This paper will briefly characterize turbo and turbo-like codes, examine their implications for physical layer system design, and discuss standards and systems where they are being used. The emphasis will be on telecommunications applications, particularly wireless, though others are mentioned. Some thoughts on the use of turbo and turbo-like codes in the future will also be given.