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Union bound evaluation for non-binary turbo coded modulations

Rami Klaimi 1, 2 Charbel Abdel Nour 1, 2 Catherine Douillard 1, 2 Joumana Farah 3
2 Lab-STICC_IMTA_CACS_IAS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : A method to compute the truncated union bound of non-binary turbo codes mapped to high order modulations is proposed in this letter. It calls for the estimate of the truncated Euclidean distance spectrum. To this end, we identify the error events that limit the Euclidean distance of non-binary turbo codes based on memory-1 convolutional codes defined over GF(q), q > 2. Application examples are elaborated for codes over GF(64). The resulting bounds are found to accurately predict the asymptotic performance of the coded modulation scheme.
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Rami Klaimi, Charbel Abdel Nour, Catherine Douillard, Joumana Farah. Union bound evaluation for non-binary turbo coded modulations. IEEE Communications Letters, Institute of Electrical and Electronics Engineers, In press, ⟨10.1109/LCOMM.2020.2980268⟩. ⟨hal-02502303⟩

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