tailieunhanh - Lecture Digital communication systems - Lecture 5

In this chapter we will discuss: History, newspapers in the digital age, defining features of newspapers, organization of the newspaper industry, newspaper ownership, producing the print and online newspaper, economics, feedback. | m oa 00 00 00 00 00 00 oo QO INTRODUCTION TO EECS II DIGITAL COMMUNICATION SUSTEMS Fall 2012 Lecture 5 Error correction for linear block codes - Syndrome decoding Burst errors and interleaving Fall 2012 Lecture 5 Slide 1 Matrix Notation for Linear Block Codes Task given k-bit message compute n-bit codeword. We can use standard matrix arithmetic modulo 2 to do the job. For example here s how we would describe the 9 4 4 rectangular code that includes an overall parity bit. D G C n 0 0 0 1 0 1 0 11 1 ỈD1 D D 01001001 00100110 000101011 1xk kxn message generator vector matrix D1 D2 D3 D P P2 P3 P4 P5 1xn code word vector in the row space of G The generator matrix Gkxcn k xk A . . kx n-k Fall 2012 Lecture 5 Slide 2 A closer look at the Parity Check Matrix A Parity equation Parity relation k P 2 Da i 1 k P 2 DAj- 0 i 1 A a So entry a in i-th row j-th column of A specifies whether data bit Di is used in constructing parity bit Pj Questions Can two columns of A be the same Should two columns of A be the same How about rows Fall 2012 Lecture 5 Slide