Turbodecoding

Turbodecoding is a powerful error-correction technique used in digital communications. It is based on a class of iterative decoding algorithms that can approach the theoretical limits of reliable communication, known as the Shannon limit. The core idea of turbodecoding is to employ two or more simple decoders that exchange information iteratively, improving the estimate of the transmitted data with each pass.

The most common turbodecoders utilize recursive systematic convolutional (RSC) codes. The transmitted data is encoded by two RSC encoders, often with a different permutation of the input bits applied to the second encoder. These encoded streams are then interleaved and transmitted. At the receiver, the received signal is passed to two decoders, each processing one of the encoded streams.

Each decoder produces a "soft" output, which is a probabilistic estimate of each bit. This soft output is then passed to the other decoder as a "prior" or "extrinsic" information. This extrinsic information helps the second decoder make a better decision about the original bits, and its improved estimate is then fed back to the first decoder. This process of exchanging information is repeated for a fixed number of iterations. With each iteration, the probability of correctly decoding the original data increases.

Turbodecoding is known for its excellent performance, especially at low signal-to-noise ratios, making it suitable for applications where bandwidth and power efficiency are critical. It has been widely adopted in various communication standards, including 3G mobile telephony (UMTS), satellite communications, and Wi-Fi. The complexity of turbodecoders is higher than traditional block codes, but their superior error-correction capabilities justify their use in many modern systems.