Source Coding

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Entropy of information sources: H ( x) In general, general ⇒ = 8 ∑ i i= 1 p i log p i = 2. 75 bit symbol H ( x) N ≥ , n : size of the code alphabet p llog n Entropy codeword d d provides llength h the ffor lower a source bound code d of the average 6
Only when = ⇒ = ⇒ − Ni n N H (x) pf: H x pi p log ) ( − N pi n M = ∑ i= 1 M = −∑ i= 1 M n i i log n −N −N i M −N i = ∑ Ni n (log n) = (log n) ∑ N i= 1 M M = ∑ Ni pi = ∑ N i= 1 i= 1 H ( x ) ∴ N = log n i n −N i i= 1 i n 100% efficiency bbe occurredd only l −N when the iis a negtive ti of n. i prob. dist. power 7
Page 1 and 2: Source Coding Prof. Ja-Ling Wu Depa
Page 3 and 4: ( i) ( i) message g X , X , , X ( i
Page 5: 01 { 1110 {{{ 1100 101 00 { 100 { u
Page 9 and 10: Theorem : Let a code have codeword
Page 11 and 12: C2 C3 C4 C5 S1 00 0 0 1 S2 01 10 01
Page 13 and 14: i l r S S − + ⇒ i i i i i r S S
Page 15 and 16: − ar ary nnumber mber representa
Page 17 and 18: Noise in Huffman coding Probabiliti
Page 19 and 20: the resort to we (2), and (1) , on
Page 21 and 22: Ex: p 1 = 0.4, p 2 = 0.2, p 3 = 0.2
Page 23: ) 2 2 3 ( 2 0 ) 2 2 2 ( 2 0 ) 2 2 1

Source Coding

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