lect1 - Error Correcting Codes Combinatorics Algorithms and...

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Error Correcting Codes: Combinatorics, Algorithms and Applications (Fall 2007) Lecture 1: Introduction August 27, 2007 Lecturer: Atri Rudra Scribe: Atri Rudra 1 Overview Error-correcting codes (or just codes) are clever ways of representing data so that one can recover the original information even if parts of it are corrupted. The basic idea is to judiciously introduce redundancy so that the original information can be recovered even when parts of the (redundant) data have been corrupted. Perhaps the most natural and common application of error correcting codes is for commu- nication. For example, when packets are transmitted over the Internet, some of the packets get corrupted or dropped. To deal with this, multiple layers of the TCP/IP stack use a form of error correction called CRC Checksum [4]. Codes are used when transmitting data over the telephone line or via cell phones. They are also used in deep space communication and in satellite broadcast (for example, TV signals are transmitted via satellite). Codes also have applications in areas not directly related to communication. For example, codes are used heavily in data storage. CDs and DVDs work fine even in presence of scratches precisely because they use codes. Codes are used in Redundant Array of Inexpensive Disks (RAID) [3] and error correcting memory [2]. Codes are also deployed in other applications such as paper bar codes, for example, the bar code used by UPS called MaxiCode [1]. In this course, we will mainly think of codes in the communication scenario. In this framework,
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lect1 - Error Correcting Codes Combinatorics Algorithms and...

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