IEEE Transactions on Information Theory · 1996 · 1.1K citations · 22 references
EngineeringComputer EngineeringComputer ScienceAlgorithmsComputer ArchitectureTheory Of ComputationChannel CapacityChannel CodingCoding TheoryCommunication ComplexityError Control CodingError-correcting CodesBit Error RateBit-error Rate AnalysisConvolutional CodesDecoding AlgorithmsEncodersError BoundingIterative DecodingTurbo Codes
A parallel concatenated coding scheme links two systematic encoders with an interleaver, scrambles the input bits before the second encoder, and produces a codeword that contains the input bits and parity bits from both encoders; this construction generalizes to any number of constituent codes and, when two convolutional codes are used with an iterative decoding algorithm of comparable complexity, achieves remarkable coding gains close to theoretical limits, giving rise to the term “turbo codes.” The authors propose a method to evaluate an upper bound on the bit‑error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length. They then apply this analytical bounding technique to illuminate key questions that have circulated in the communications community since the introduction of turbo codes.
A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes, have been previously shown to yield remarkable coding gains close to theoretical limits. They have been named, and are known as, "turbo codes". We propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length. The analytical bounding technique is then used to shed some light on some crucial questions, which have been floating around in the communications community since the proposal of turbo codes.
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