Turbokoodit

Turbokoodit, known in English as turbo codes, are a class of error-correcting codes designed to approach the Shannon limit for reliable data transmission. They use a parallel concatenation of two recursive systematic convolutional encoders connected by an interleaver, producing codewords that combine systematic bits with parity information. The interleaver rearranges the input sequence between the encoders to create complementary redundancy and improve error resilience.

Encoding involves sending the original data through one convolutional encoder while sending a permuted version of the data through a second encoder. The outputs include two parity streams and the systematic bits. The resulting code rate depends on the number of parity bits; common configurations yield rates such as 1/2 or 2/3.

Decoding relies on iterative soft-decision decoding. Each constituent decoder runs a BCJR algorithm to produce posterior probabilities, then exchanges extrinsic information with the other decoder. Through several iterations, the estimates are refined, yielding performance close to the theoretical limit for practical block lengths. The effectiveness depends on the memory of the constituent encoders and the design of the interleaver, which affects how well errors are dispersed between iterations.

History and impact: Turbo codes were introduced in 1993 by Berrou, Glavieux, and Thitimajshima, demonstrating near-capacity performance and catalyzing extensive research in coding theory. They have influenced numerous mobile communications standards and data storage applications, where high reliability is needed without excessive bandwidth. Variants and optimizations—such as different interleaver designs and decoder implementations—continue to be explored in both academia and industry.

See also: turbo codes; parallel concatenated convolutional codes; iterative decoding.