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Multidimensional Dataflow Graphs

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Abstract

In many signal processing applications, the tokens in a stream of tokens have a dimension higher than one. For example, the tokens in a video stream represent images so that a video application is actually three- or four-dimensional: Two dimensions are required in order to describe the pixel coordinates, one dimension indexes the different color components, and the time finally corresponds to the last dimension. Static multidimensional (MD) streaming applications can be modeled using one-dimensional dataflow graphs[7], but these are at best cyclostatic dataflow graphs, often with many phases in the actor’s vector valued token production and consumption patterns. These models incur a high control overhead. Furthermore such a notation hides many important algorithm properties such as inherent data parallelism, fine grained data dependencies and thus required memory sizes. Finally, the model is very implementation specific in that some of the degrees of freedom such as the processing order are already nailed down and cannot be changed easily without completely recreating the model.

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Notes

  1. 1.

    This restriction will be released in Sect. 7.

  2. 2.

    For more than two dimensions, see [12].

  3. 3.

    Note that this relation will be broken in Sect. 7

  4. 4.

    Section 3 introduced a processing order to enumerate sample points that are not part of a rectangular grid. This section differs in that it considers rectangular instead of arbitrary sampling patterns. The defined processing orders are hence purely to describe the application behavior, and are not a prerequisite for the balance equation.

  5. 5.

    For Fig. 10b, a first level block with two rows and one column generates the desired processing order.

  6. 6.

    While the stretching depicted in Fig. 12c improves the situation, actor B still oscillates between a period of activity with three firings and a period with no activity. To solve this problem, more aggressive stretching techniques are discussed in [12].

  7. 7.

    Mathematically, this can be expressed by the lexicographic order. See [16] as well as [12] for more details.

  8. 8.

    Now Thales.

References

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Authors and Affiliations

  1. Fraunhofer Institute for Integrated Circuits, Erlangen, Germany

    Joachim Keinert

  2. Leiden University, Leiden, the Netherlands

    Ed F. Deprettere

Authors
  1. Joachim Keinert
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  2. Ed F. Deprettere
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Correspondence to Joachim Keinert .

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Editors and Affiliations

  1. , Dept. of Electrical and, University of Maryland, A. V. Williams Bldg. 2311, College Park, 20742, Maryland, USA

    Shuvra S. Bhattacharyya

  2. Leiden Inst. Advanced Computer Science, Leiden Embedded Research Center, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

    Ed F. Deprettere

  3. Software for Systems on Silicon, RWTH Aachen University, Templergraben 55, Aachen, 52056, Germany

    Rainer Leupers

  4. , Department of Pervasive Computing, Tampere University of Technology, Korkeakoulunkatu 1, Tampere, 33720, Finland

    Jarmo Takala

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Keinert, J., Deprettere, E.F. (2013). Multidimensional Dataflow Graphs. In: Bhattacharyya, S., Deprettere, E., Leupers, R., Takala, J. (eds) Handbook of Signal Processing Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6859-2_35

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  • DOI: https://doi.org/10.1007/978-1-4614-6859-2_35

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