Recursively Indexed Quantization of Memoryless Sources

1. Recursively Indexed Quantization of Memoryless Sources Author: Khalid Sayood, member IEEE Sangsin Na, member IEEE IEEE Transactions of Information theory Vol. 38, No. 5, Sep. 92 • Reporter: ChiaHsing Lee, 8817586 • NCTU CSIE

2. Outline • Source coding scheme • Recursive indexing scheme • Recursive index quantizer • Analysis of rate and distortion • Conclusion

3. x y z Q Binary Encoder Source coding scheme • Encoder of source coding • Complexity of binary encoder • More input alphabets(y), more operations needed. • Reduce alphabets size may introduce distortion of quantization

4. Recursive indexing scheme • An modulo operation • Given 2 sets , • such that if i = mK + R • In inverse,

5. Recursively indexed quantizer • Definition • Given • Quantizer of size K, step size , and are the smallest and largest output levels

6. Recursively indexed quantizer • Q(x) = • Nearest output level, Q(x) • If • , where • If , and • , where • If , and

7. Quantize and recursively index • y be the output levels of , i.e , • if • if

8. Analysis of distortion • Distortion of quantizer • Granular error • applied to source with • Overload error • no

9. Analysis of rate • Rate is determined by binary encoder • Fixed-to-fixed length • Another mapping relation • Fixed-to-variable length • Such like huffman coding or arithmetic coding

10. Analysis of rate • Fixed-to-fixed length • Let be the number of symbols to represent level j • , j=1, 2, ..(N-1),

11. Rate of recursively indexed quantizer • Fixed-to-variable length

12. Numerical Result • RD curve for various size of Laplacian source

13. Numerical Result

14. Conclusion • Advantage • Avoid overload distortion • Reduce distortion • Reduce the input of binary encoder • Reduce encoder complexity • Need not modified original encoder