Lect2 - Error Correcting Codes Combinatorics Algorithms and Applications(Fall 2007 Lecture 2 Error Correction and Channel Noise Lecturer Atri Rudra

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Error Correcting Codes: Combinatorics, Algorithms and Applications (Fall 2007) Lecture 2: Error Correction and Channel Noise August 29, 2007 Lecturer: Atri Rudra Scribe: Yang Wang & Atri Rudra As was mentioned in the last lecture, the fundamental tradeoff we are interested in for this course is the one between the amount of redundancy in the code vs. the number of errors that it can correct. We defined the notion of rate of a code to capture the amount of redundancy. However, before we embark on a systematic study of the tradeoff above, we need to formally define what it means to correct errors. We do so next. 1 Error correction Before we define what we mean by error correction, we formally define the notion of encoding . Definition 1.1 (Encoding function). Let . An equivalent description of the code is by an injective mapping called encoding function. Next we move to error correction. Intuitively, we can correct a received word if we can recover the transmitted codeword (or equivalently the corresponding message). This “reverse” process is achieved by decoding . Definition 1.2 (Decoding function). Let be a code. A mapping is called a decoding function for . The definition of a decoding function by itself does not give anything interesting. What we really need from a decoding function is that it recovers the transmitted message. This notion is captured next. Definition 1.3 (Error Correction). Let and let be an integer. is said to be- error-correcting if there exists a decoding function such that for every error message and error pattern with at most errors, . Figure 1 illustrates how the definitions we have examined so far interact. We will also very briefly look at a weaker form of error recovery called error detection ....
View Full Document

This note was uploaded on 10/16/2011 for the course ELECTRICAL EE251202 taught by Professor Rejaei during the Spring '10 term at Sharif University of Technology.

Page1 / 4

Lect2 - Error Correcting Codes Combinatorics Algorithms and Applications(Fall 2007 Lecture 2 Error Correction and Channel Noise Lecturer Atri Rudra

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online