Lecture Notes and Examples - 11/23/15
Lecture Notes and Examples - 11/23/15 MAT 1000-001
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This 6 page Class Notes was uploaded by Josh Desotell on Tuesday November 24, 2015. The Class Notes belongs to MAT 1000-001 at Wayne State University taught by Daniel Isaksen in Summer 2015. Since its upload, it has received 40 views. For similar materials see (MC) Math in Today's World in Mathematics (M) at Wayne State University.
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Eugh...this class is soo hard! I'm so glad that you'll be posting notes for this class
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Date Created: 11/24/15
1 12 315 Lecture Notes VariableLength Code In binary linear codes every code word has the same length This can be inef cient if some code words are more common than others A variablelength code is a code in which the code word lengths are not all the same EX Morse code is a variablelength code Data Compression Use a scheme in which the more frequently occurring data are represented by fewer bits This can save space and make shorter transmissions EX ZlP GIF JPEG are data compression algorithms Data compression is especially important for phots videos and music which contain a very large amount of data Genetic Data Compression Genes are sequences of the four nucleotides A T G and C EX AAACAGTAAC A is most common C is next most common and T and G are slightly rarer Encode gene sequences are AO C1O T110 G111 Gene Uncompressind To decode a binary string to a sequence Work from left to right Break the binary string into code words 0 10 110 and 111 Convert each code word to A C T and G Huffman Coding Huffman codes are ef cient for encoding data composed of symbols with variable frequencies 1 List the symbols with the eas probable rst 2 Merge the two least probable symbols with the least probable on the left 3 Reorder the list and repeat 4 Construct a tree that represents the merging process 5 Label the branches with Os and ls 6 Determine code words for each symbol from the tree 112315 Lecture Examples Ex 1 Encode gene Sequences 115m ACTS n a AAACAGT Demde the binaw 517mg 3 l llilll l Tye4 7 0 Q J4 OJOJ H 1 1 1 0 aUlm a E113 A date set eetneiste 01f symbele A B E 1 1E and F Frequencies A 1125 B 01351 C 13215 1 013 E 132113 IF an Cenetmct the Huffman Cecile a B 03 gt m 7 A WP 13 quot 5 W m E 4 0 7 1 L13 L C 39 51 075C4ig PDQ459539 C 1 39 N N E I E m pig 349 M 1 f ELILILY 3J J7