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Stage majority multiplexing and nonlinear turbo codes


S.S. Volkov, B.V. Roshchin, A.B. Roshchin

The article deals with perspective methods of binary signals multiplexing, based on majority function. These methods allow to combine signals multiplexing with high performance forward error correction comparable to well-known linear block codes, such as BCH and Reed-Solomon codes as well as convolutional codes with Viterby decoding. Considerable advantage of stage majority multiplexing is a possibility to deal with sources both with equal and different performance. Another important feature is either hard or soft decision demultiplexing (decoding). The following aspects are considered in the article: methods of channel signals based on Walsh functions generation, schemes of multiplexing and demultiplexing both for nonredundant coding and redundant coding with a possibility of error correction. It's proposed in the article to use stage multiplexing for reducing complexity and redundancy. According to this scheme multiplexing modules are bunching in groups of three, aggregate signal goes to one module of the next stage. This process is continued up to the final stage at which final aggregate signal is forming. Later in the article conceptions of constant and variable number of stages are introduced and discussed. It's shown that multiplexing schemes with variable number of stages allows to sufficiently reduce the redundancy comparing to schemes with constant number of stages. In conclusion an average bit error rate for a scheme with variable number of stages is calculated. According to this calculation the following conclusion is made: the codes based on stage majority multiplexing schemes with variable number of stages allow to get tiny bit error rate along with finite redundancy.
  1. Gridin V.N., Mazepa R.B., Roshhin B.V. Mazhoritarnoe uplotnenie i kodirovanie dvoichny'x signalov. M.: Nauka. 2001.

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