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411 | 411 | "source": [
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412 | 412 | "As can be seen, the `Mapper` class inherits from `Layer`, i.e., implements a Keras layer.\n",
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413 | 413 | "\n",
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414 |
| - "This allows to simply built complex systems by using the [Keras functional API](https://keras.io/guides/functional_api/) to stack layers." |
| 414 | + "This allows to simply build complex systems by using the [Keras functional API](https://keras.io/guides/functional_api/) to stack layers." |
415 | 415 | ]
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416 | 416 | },
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417 | 417 | {
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521 | 521 | "id": "aca7a98b",
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522 | 522 | "metadata": {},
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523 | 523 | "source": [
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524 |
| - "In *Eager* mode, we can directly access the values of each tensor. This simplify debugging." |
| 524 | + "In *Eager* mode, we can directly access the values of each tensor. This simplifies debugging." |
525 | 525 | ]
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526 | 526 | },
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527 | 527 | {
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613 | 613 | "id": "bfc184ba-c090-4443-9cd6-c217b3f64052",
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614 | 614 | "metadata": {},
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615 | 615 | "source": [
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616 |
| - "It is typically more convenient to wrap a Sionna-based communication system into a [Keras models](https://keras.io/api/models/model/).\n", |
| 616 | + "It is typically more convenient to wrap a Sionna-based communication system into a [Keras model](https://keras.io/api/models/model/).\n", |
617 | 617 | "\n",
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618 | 618 | "These models can be simply built by using the [Keras functional API](https://keras.io/guides/functional_api/) to stack layers.\n",
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619 | 619 | "\n",
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854 | 854 | "metadata": {},
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855 | 855 | "source": [
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856 | 856 | "One of the fundamental paradigms of Sionna is batch-processing.\n",
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857 |
| - "Thus, the example above could be executed with for arbitrary batch-sizes to simulate `batch_size` codewords in parallel.\n", |
| 857 | + "Thus, the example above could be executed for arbitrary batch-sizes to simulate `batch_size` codewords in parallel.\n", |
858 | 858 | "\n",
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859 | 859 | "However, Sionna can do more - it supports *N*-dimensional input tensors and, thereby, allows the processing of multiple samples of multiple users and several antennas in a single command line.\n",
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860 |
| - "Let's say we want to encoded `batch_size` codewords of length `n` for each of the `num_users` connected to each of the `num_basestations`. \n", |
| 860 | + "Let's say we want to encode `batch_size` codewords of length `n` for each of the `num_users` connected to each of the `num_basestations`. \n", |
861 | 861 | "This means in total we transmit `batch_size` * `n` * `num_users` * `num_basestations` bits."
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862 | 862 | ]
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863 | 863 | },
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