Fundamentals of Turbo Codes

Mar 15, 2002

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In 1948, Claude Shannon proved the existence of techniques that could provide a coding gain of 11-12 dB. Forty years later, the error-correction coding discipline seemed to have reached a coding-gain plateau of about 6 dB. In 1993, a remarkable discovery gave rise to turbo codes that can provide about 10 dB of coding gain (most of what Shannon had predicted). In the year 2002, turbo coding represents the key research topic among all error-correcting research. This article starts with fundamental likelihood and decision-making concepts, and uses simple examples to explain the benefits of these codes.

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Introduction

Concatenated coding schemes were first proposed by G. D. Forney, Jr. in Concatenated Codes (MIT Press) as a method for achieving large coding gains by combining two or more relatively simple building-block or component codes (sometimes called constituent codes). The resulting codes had the error-correction capability of much longer codes, and they were endowed with a structure that permitted relatively easy to moderately complex decoding. A serial concatenation of codes is most often used for power-limited systems such as transmitters on deep-space probes. The most popular of these schemes consists of a Reed-Solomon outer (applied first, removed last) code followed by a convolutional inner (applied last, removed first) code. A turbo code can be thought of as a refinement of the concatenated encoding structure plus an iterative algorithm for decoding the associated code sequence.

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