Toward an Algebraic Theory for Turbo Codes
نویسنده
چکیده
Instead of a random interleaver, an algebraic interleaver interconnecting two simple convolutional codes with feedback encoders forms an algebraic quasi-cyclic code. An (nC , k) convolutional code in tailbiting form becomes a quasi-cyclic (QC) linear code of length LnC for some L = Mn. Interleavers with a period M connect two such codes to produce a QC turbo code. The QC turbo codes check equations are transformed and analyzed on an extension field of GF (2) with an nth root of unity. Analysis of the QC turbo code gives insight into the minimum distance of the standard turbo code derived from it.
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