# lect24 - Error Correcting Codes Combinatorics Algorithms...

This preview shows pages 1–2. Sign up to view the full content.

Error Correcting Codes: Combinatorics, Algorithms and Applications (Fall 2007) Lecture 24: Code concatenation October 24, 2007 Lecturer: Atri Rudra Scribe: Yang Wang Recall the following question we have encountered before: Question 0.1. Is there an explicit asymptotically good code? (that is, rate R > 0 and relative distance δ > 0 for small q ). Here, explicit means: (i) polynomial time construction (of some representation of the code), (ii) “super” explicit (like description of RS code). We will answer the question at least in the sense of explicit codes of (i) in this lecture. 1 Code Concatenation Code concatenation was first proposed by Forney[1]. For q 2 , k 1 and Q = q k , consider two codes which we call outer code and inner code: C out : [ Q ] K [ Q ] N , C in : [ q ] k [ q ] n . Note that the alphabet size of C out exactly matches | C in | . Then given m = ( m 1 , . . . , m K ) [ Q ] K , we have the code C out C in : [ q ] kK [ q ] nN defined as C out C in ( m ) = ( C in ( C out ( m ) 1 ) , . . . , C in ( C out ( m ) N )) , where C out ( m ) = C out ( m ) 1 , . . . , m ) N . This construction is also illustrated in Figure 1. We now look at some properties of a concatenated codes.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern