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 + + 1005030ab17cdefgh0210122100261ij01Př. 1 \ No newline at end of file diff --git a/KIV TI/Cvičení/Cviceni08.md b/KIV TI/Cvičení/Cviceni08.md new file mode 100644 index 0000000..29b1c23 --- /dev/null +++ b/KIV TI/Cvičení/Cviceni08.md @@ -0,0 +1,26 @@ +**Př. 1**: Zdroj generuje znaky z abecedy $\{a, b, c, d, e, f, g, h, i, j\}$. Pravděpodobnosti jejich výskytů jsou 20 %, 18 %, 15 %, 12 %, 10 %, 8 %, 7 %, 4 %, 4 %, 2 %. Cílová abeceda kódu je $\{0, 1, 2\}$. + +Kroky +- seřadit podle pravděpodobností +- začínám od posledních dvou + - sečtu jejich pravděpodobnost ($2+4 = 6$) + - zařadím ji do tabulky +- pokračuji vždy se třemi dolními prvky + - $4+6+7 = 17$ + - $8 + 10 + 12 = 30$ + - $15+17+18 = 50$ + - $20+30+50 = 100$ +- vznikl strom + +| znak | pravděpodobnost | kód | +| ---- | --------------- | ---- | +| a | 20 | 2 | +| b | 18 | 00 | +| c | 15 | 02 | +| d | 12 | 10 | +| e | 10 | 11 | +| f | 8 | 12 | +| g | 7 | 010 | +| h | 4 | 012 | +| i | 4 | 0110 | +| j | 2 | 0111 | diff --git a/KIV TI/Cvičení/Cviceni09.md b/KIV TI/Cvičení/Cviceni09.md new file mode 100644 index 0000000..2e406d4 --- /dev/null +++ b/KIV TI/Cvičení/Cviceni09.md @@ -0,0 +1,168 @@ +**Př. 1**: Uvažujme lineární prostor $\mathbb{Z}_{2}^5$ (množina pětic tvořených z 0 a 1). Slova předpokládáme jako $x_{1} x_{2} x_{3} x_{4} x_{5}$. + +1) všechna slova splňující podmínku $x_{2} + x_{3} = x_{5}$ + - nulový prvek $00000$ - platí + - $x_{2} + x_{3} = 0 + 0 = 0 = x_{5}$ + - sčítání - platí + - $x_{1} x_{2} x_{3} x_{4} x_{5} \quad x_{2} + x_{3} = x_{5}$ + - $y_{1} y_{2} y_{3} y_{4} y_{5} \quad y_{2} + y_{3} = y_{5}$ + - $(x_{1}+y_{1}) (x_{2}+y_{2}) (x_{3}+y_{3}) (x_{4}+y_{4}) (x_{5}+y_{5})$ + - $(x_{2}+y_{2}) + (x_{3}+y_{3}) \,?\, (x_{5}+y_{5})$ + - $L = x_{2}+y_{2}+x_{3}+y_{3} = (x_{2}+y_{2})+(x_{3}+y_{3}) = x_{5}+y_{5}$ +2) všechna slova splňující podmínku $x_{2} + x_{3} = 1$ + - nulový prvek $00000$ - neplatí! + - není lineární kód +3) všechna slova s méně než třemi 1 + - sčítání - neplatí + - $11000$ + - $00110$ + - $11110$ (nepatří) + +**Př. 2**: Pro lineární kód 1 určíme dimenzi, bázi, kontrolní rovnici a generující i kódovou matici. + +- dimenze = 4 + - $x_{5}$ je zabezpečovací prvek + - zbytek prvků (4) je informační +- báze + - kanonická báze + - poté dopočítám poslední prvek + - $[10000]^T$ + - $[01001]^T$ + - $[00101]^T$ + - $[00010]^T$ +- kontrolní rovnice + - $x_{2} + x_{3} + x_{5} = 0$ + - přičtu $x_{5}$, protože v tělese $Z_{2}$ je to jako odčítání +- generující matice + - $G = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{bmatrix}$ +- kódová matice + - pokud $G = [I_{k} | B]$, tak $H = [-B^T | I_{n-k}]$ + - $H = [01101]$ + +**Př. 3**: Těleso $Z_{5}$. + +sčítací tabulka + +| + | 0 | 1 | 2 | 3 | 4 | +| --- | --- | --- | --- | --- | --- | +| 0 | 0 | 1 | 2 | 3 | 4 | +| 1 | 1 | 2 | 3 | 4 | 0 | +| 2 | 2 | 3 | 4 | 0 | 1 | +| 3 | 3 | 4 | 0 | 1 | 2 | +| 4 | 4 | 0 | 1 | 2 | 3 | + +násobící tabulka + +| * | 0 | 1 | 2 | 3 | 4 | +| --- | --- | --- | --- | --- | --- | +| 0 | 0 | 0 | 0 | 0 | 0 | +| 1 | 0 | 1 | 2 | 3 | 4 | +| 2 | 0 | 2 | 4 | 1 | 3 | +| 3 | 0 | 3 | 1 | 4 | 2 | +| 4 | 0 | 4 | 3 | 2 | 1 | + +opačné prvky: +- $-1 = 4$ +- $-2 = 3$ +- $-3 = 2$ +- $-4 = 1$ +- $-0 = 0$ + +převrácené prvky: +- $1^{-1} = 1$ +- $2^{-1} = 3$ +- $3^{-1} = 2$ +- $4^{-1} = 4$ + +**Př. 4**: Rozhodněte, zda tato matice může být generující maticí lineárního kódu. + +$$ +A = \begin{bmatrix} +1 & 4 & 1 & 1 & 1 \\ +2 & 4 & 0 & 0 & 1 \\ +0 & 2 & 1 & 1 & 0 +\end{bmatrix} \begin{array}{l} +\\ + \space 3\cdot(1) \\ \\ +\end{array} \sim \begin{bmatrix} +1 & 4 & 1 & 1 & 1 \\ +0 & 1 & 3 & 3 & 4 \\ +0 & 2 & 1 & 1 & 0 +\end{bmatrix} \begin{array}{l} +\\ \\ + \space 3\cdot(2) +\end{array} \sim \begin{bmatrix} +1 & 4 & 1 & 1 & 1 \\ +0 & 1 & 3 & 3 & 4 \\ +0 & 0 & 0 & 0 & 2 +\end{bmatrix} +$$ + +Lineárně nezávislé (pivotové) sloupce: první, druhý a pátý + +Kolik bude mít kód značek? $5^3$ +- $[000\dots]$ +- $[001\dots]$ +- $[002\dots]$ +- $\vdots$ +- $[444\dots]$ + +Závěr: +- matice bude generovat lineární kód, ale nebude systematický +- pro nalezení systematického kódu je potřeba provést permutaci sloupců + - $A' = [A_{1}A_{2}A_{5}A_{3}A_{4}]$ + - v této matici provedeme GJEM a dostaneme se k systematickému tvaru generující matice + +$$ +A' = \begin{bmatrix} +1 & 4 & 1 & 1 & 1 \\ +0 & 1 & 4 & 3 & 3 \\ +0 & 0 & 2 & 0 & 0 +\end{bmatrix} \begin{array}{l} ++ \space (2) \\ + \space 3 \cdot (3) \\ \cdot \space 3 +\end{array} \sim \left[\begin{array}{ccc:cc} +1 & 0 & 0 & 4 & 4 \\ +0 & 1 & 0 & 3 & 3 \\ +0 & 0 & 1 & 0 & 0 +\end{array}\right] = G' +$$ + +$$ +H' = \left[\begin{array}{ccc:cc} +1 & 2 & 0 & 1 & 0 \\ +1 & 2 & 0 & 0 & 1 +\end{array}\right] +$$ + +**Př. 5**: Těleso $Z_{3}$. + +$$ +G = \begin{bmatrix} +1 & 1 & 1 & 1 & 1 \\ +0 & 1 & 1 & 1 & 1 \\ +1 & 1 & 0 & 0 & 0 +\end{bmatrix} +$$ + +Určete kontrolní rovnice a kontrolní matici. + +Kontrolní matice +- předpokládáme obecný řádek kontrolní matice $[h_{1} h_{2} h_{3} h_{4} h_{5}]$ +1. $h_{1} + h_{2} + h_{3} + h_{4} + h_{5} = 0$ +2. $h_{2} + h_{3} + h_{4} + h_{5} = 0$ +3. $h_{1} + h_{2} = 0$ +- dosadíme řádek do řádku +4. $h_{3} + h_{4} + h_{5} = 0$ +- $h_{3} = - h_{4} - h_{5}$ +- $h_{3} + 2h_{4} + 2h_{5}$ + +$$ +H = \left[\begin{array}{ccc:cc} +0 & 0 & 1 & 1 & 0 \\ +0 & 0 & 2 & 0 & 1 +\end{array}\right] +$$ + +sloupce v matici $H$ jsou $h_{1}, h_{2}, h_{3}, h_{4}, h_{5}$ + +Kontrolní rovnice +- $2v_{3} + v_{4} = 0$ +- $2v_{3} + v_{5} = 0$ \ No newline at end of file