![\"\"](\"http:\/\/ccom.uprrp.edu\/~labemmy\/Wordpress\/wp-content\/uploads\/2010\/11\/binary-code.jpg\")
<\/p>\nA main goal of coding theory is the design of coding methods that achieve error control: detect and correct errors in received and stored data.<\/em><\/h4>\n<\/div>\n<\/p>\n
<\/p>\n
\nProjects<\/mark><\/a><\/h2>\n\n- Balanced Functions<\/mark><\/a><\/em><\/li>\n<\/ul>\n
\n- Turbo Codes<\/mark><\/a><\/em><\/li>\n<\/ul>\n
\n- Other<\/mark><\/a><\/em><\/li>\n<\/ul>\n<\/div>\n
<\/p>\n
\nCoding Theory<\/strong> is the study of methods for efficient and accurate transmission or storage of information. It started out as a mathematical and engineering subject with the paper “A Mathematical Theory of Communication” by Claude Shannon<\/em> in 1948.<\/p>\nConsider the next image which represents a general information transmission system:
\n![\"\"](\"http:\/\/ccom.uprrp.edu\/~labemmy\/Wordpress\/wp-content\/uploads\/2010\/10\/new_General-Information-Transmission-System-1024x284.jpg\")
<\/p>\n
The information that is transmitted or stored is called the message<\/em>. A channel<\/em> is the physical medium through which the information is transmitted or where it is stored. Telephone lines and the atmosphere are examples of channels. An encoder<\/em> adds redundancy to the message by constructing codewords so that, when received, the decoder<\/em> can detect and correct errors. The code<\/em> is the set of all codewords.<\/p>\nMost importantly, Coding Theory deals with the problem of detecting and correcting transmission errors caused by disturbances on the channel called noise.<\/strong><\/em><\/h3>\nNoise may be caused by sunspots, lighting, folds in magnetic tape, meteor showers, competing telephone messages, random radio disturbance, or many other things.<\/p>\n
Example<\/strong>: Suppose we want to send the message “1”. We can encode this by repeating it, say 3 times, so the codeword would be “111”. Now suppose the codeword is sent through a channel and “101” was received. The decoder knows that the codeword has the message repeated 3 times and decides on the message based on the received symbol that occurred most frequently.![\"\"](\"http:\/\/ccom.uprrp.edu\/~labemmy\/Wordpress\/wp-content\/uploads\/2010\/10\/example.jpg\" "\\"example\\"")
<\/p>\nThe most common applications for Coding Theory include:<\/strong><\/em><\/h3>\n\n- transmission of data (telephone lines, internet ,networks)<\/li>\n
- wireless communication<\/li>\n
- communication with deep space exploration crafts (Mariner, Voyager, etc. \u2013 the most important early application)<\/li>\n
- storing\/retrieving information in computer memory<\/li>\n
- storing\/retrieving audio\/video information (CDs, DVDs and Blu-Ray disks)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
A main goal of coding theory is the design of coding methods that achieve error control: detect and correct errors in received and stored data. Projects Balanced Functions Turbo Codes Other Coding Theory is the study of methods for efficient … Continue reading
Projects<\/mark><\/a><\/h2>\n\n- Balanced Functions<\/mark><\/a><\/em><\/li>\n<\/ul>\n
\n- Turbo Codes<\/mark><\/a><\/em><\/li>\n<\/ul>\n
\n- Other<\/mark><\/a><\/em><\/li>\n<\/ul>\n<\/div>\n
<\/p>\n
\nCoding Theory<\/strong> is the study of methods for efficient and accurate transmission or storage of information. It started out as a mathematical and engineering subject with the paper “A Mathematical Theory of Communication” by Claude Shannon<\/em> in 1948.<\/p>\nConsider the next image which represents a general information transmission system:
\n<\/p>\n
The information that is transmitted or stored is called the message<\/em>. A channel<\/em> is the physical medium through which the information is transmitted or where it is stored. Telephone lines and the atmosphere are examples of channels. An encoder<\/em> adds redundancy to the message by constructing codewords so that, when received, the decoder<\/em> can detect and correct errors. The code<\/em> is the set of all codewords.<\/p>\nMost importantly, Coding Theory deals with the problem of detecting and correcting transmission errors caused by disturbances on the channel called noise.<\/strong><\/em><\/h3>\nNoise may be caused by sunspots, lighting, folds in magnetic tape, meteor showers, competing telephone messages, random radio disturbance, or many other things.<\/p>\n
Example<\/strong>: Suppose we want to send the message “1”. We can encode this by repeating it, say 3 times, so the codeword would be “111”. Now suppose the codeword is sent through a channel and “101” was received. The decoder knows that the codeword has the message repeated 3 times and decides on the message based on the received symbol that occurred most frequently.<\/p>\nThe most common applications for Coding Theory include:<\/strong><\/em><\/h3>\n\n- transmission of data (telephone lines, internet ,networks)<\/li>\n
- wireless communication<\/li>\n
- communication with deep space exploration crafts (Mariner, Voyager, etc. \u2013 the most important early application)<\/li>\n
- storing\/retrieving information in computer memory<\/li>\n
- storing\/retrieving audio\/video information (CDs, DVDs and Blu-Ray disks)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
A main goal of coding theory is the design of coding methods that achieve error control: detect and correct errors in received and stored data. Projects Balanced Functions Turbo Codes Other Coding Theory is the study of methods for efficient … Continue reading
- \n
- Turbo Codes<\/mark><\/a><\/em><\/li>\n<\/ul>\n
- \n
- Other<\/mark><\/a><\/em><\/li>\n<\/ul>\n<\/div>\n
<\/p>\n
\nCoding Theory<\/strong> is the study of methods for efficient and accurate transmission or storage of information. It started out as a mathematical and engineering subject with the paper “A Mathematical Theory of Communication” by Claude Shannon<\/em> in 1948.<\/p>\n
Consider the next image which represents a general information transmission system:
\n<\/p>\nThe information that is transmitted or stored is called the message<\/em>. A channel<\/em> is the physical medium through which the information is transmitted or where it is stored. Telephone lines and the atmosphere are examples of channels. An encoder<\/em> adds redundancy to the message by constructing codewords so that, when received, the decoder<\/em> can detect and correct errors. The code<\/em> is the set of all codewords.<\/p>\n
Most importantly, Coding Theory deals with the problem of detecting and correcting transmission errors caused by disturbances on the channel called noise.<\/strong><\/em><\/h3>\n
Noise may be caused by sunspots, lighting, folds in magnetic tape, meteor showers, competing telephone messages, random radio disturbance, or many other things.<\/p>\n
Example<\/strong>: Suppose we want to send the message “1”. We can encode this by repeating it, say 3 times, so the codeword would be “111”. Now suppose the codeword is sent through a channel and “101” was received. The decoder knows that the codeword has the message repeated 3 times and decides on the message based on the received symbol that occurred most frequently.
<\/p>\nThe most common applications for Coding Theory include:<\/strong><\/em><\/h3>\n
- \n
- transmission of data (telephone lines, internet ,networks)<\/li>\n
- wireless communication<\/li>\n
- communication with deep space exploration crafts (Mariner, Voyager, etc. \u2013 the most important early application)<\/li>\n
- storing\/retrieving information in computer memory<\/li>\n
- storing\/retrieving audio\/video information (CDs, DVDs and Blu-Ray disks)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
A main goal of coding theory is the design of coding methods that achieve error control: detect and correct errors in received and stored data. Projects Balanced Functions Turbo Codes Other Coding Theory is the study of methods for efficient … Continue reading
- Other<\/mark><\/a><\/em><\/li>\n<\/ul>\n<\/div>\n