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commpy/channelcoding/README.md

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@@ -7,15 +7,15 @@ The main idea of the channel codes can be formulated as following thesises:
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- **redundant bits** are added for *error detection* and *error correction*;
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- some special algorithms (<u>coding schemes</u>) are used for this.
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<img src="https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/FECmainidea1.png" width="800" />
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<img src="https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/FECmainidea1.png" width="800" />
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The fact how "further" a certain algorithm divides the code words among themselves, and determines how strongly it protects the signal from noise [1, p.23].
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<img src="https://habrastorage.org/webt/n7/o4/bs/n7o4bsf7_htlv10gsatc-yojbrq.png" width="800" />
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In the case of binary codes, the minimum distance between all existing code words is called **Hamming distance** and is usually denoted **dmin**:
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<img src="https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/FECexamp2.png" alt="examp2" width="400"/>
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<img src="https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/FECexamp2.png" alt="examp2" width="400"/>
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## Classification
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Secondly, codes can be classified as **block** and **continuous**:
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![](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/BlockCont.png)
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![](https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/BlockCont.png)
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## Net bit rate
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Redundancy of the channel coding schemes influences (decreases) bit rate. Actually, it is the cost for the noiseless increasing.
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[**Net bit rate**](https://en.wikipedia.org/wiki/Bit_rate#Information_rate) concept is usually used:
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<img src="https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/nebitrate.png" alt="net" width="500"/>
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<img src="https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/nebitrate.png" alt="net" width="500"/>
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To change the code rate (k/n) of the block code dimensions of the Generator matrix can be changed:
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![blockcoderate](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/coderateblock.png)
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![blockcoderate](https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/coderateblock.png)
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To change the coderate of the continuous code, e.g. convolutional code, **puncturing** procedure is frequently used:
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![punct](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/punct.png)
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![punct](https://raw.githubusercontent.com/veeresht/CommPy/master/commpy/channelcoding/doc/assets/punct.png)
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## Example
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