Create README.md

Some theory basics.

Author: kirlf

commpy/channelcoding/README.md

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+# Channel codes basics
+
+## Main idea
+
+The main idea of the channel codes can be formulated as following thesises:
+- **noise immunity** of the signal should be increased;
+- **redundant bits** are added for *error detection* and *error correction*;
+- some special algorithms (<u>coding schemes</u>) are used for this.
+
+![](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/FECmainidea1.png)
+
+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].
+
+![](https://habrastorage.org/webt/n7/o4/bs/n7o4bsf7_htlv10gsatc-yojbrq.png)
+
+In the case of binary codes, the minimum distance between all existing code words is called ** Hamming distance ** and is usually denoted **dmin**:
+
+<img src="https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/FECexamp2.png" alt="examp2" width="400"/>
+
+
+## Classification
+
+Some classification is needed to talk about those or other implementations of the encoding and decoding algorithms.
+
+First, the channel codes:
+- can only [*detect*](https://en.wikipedia.org/wiki/Cyclic_redundancy_check) the presence of errors
+- and they can also [*correct* errors](https://en.wikipedia.org/wiki/Error_correction_code).
+
+Secondly, codes can be classified as **block** and **continuous**:
+
+![](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/BlockCont.png)
+
+## Net bit rate
+Redundancy of the channel coding schemes influences (decreases) bit rate. Actually, it is the cost for the noiseless increasing.
+**Net bit** rate concept is usually used:
+
+<img src="https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/nebitrate.png" alt="net" width="500"/>
+
+To change the code rate (k/n) of the block code dimensions of the Generator matrix can be changed:
+![blockcoderate](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/coderateblock.png)
+
+To change the coderate of the continuous code, e.g. [convolutional code](https://github.com/kirlf/CSP/blob/master/FEC/Convolutional%20codes%20intro.md), **puncturing** procedure is frequently used:
+
+![punct](https://raw.githubusercontent.com/kirlf/CSP/master/FEC/assets/punct.png)
+
+### Reference
+
+[1] Moon, Todd K. "Error correction coding." Mathematical Methods and Algorithms. Jhon Wiley and Son (2005).