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aya eid

on 22 May 2017

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Transcript of old

R.W Hamming had invented a code for correcting errors in communication and the Hamming code was born. Hamming was interested in two problems at once: increasing the distance as much as possible, while at the same time increasing the code rate as much as possible. During the 1940s he developed several encoding schemes that were dramatic improvements on existing codes.
what is Hamming code
2k equally likely messages can be represented by k binary digits. If these messages were not coded, then one error or more might occur. For this problem error correcting codes are used. They are a technique where more than minimum number of binary digits are used to represent the message. These extra digits called redundant or parity bits was founded to detect the errors and hopefully correct them.
A hamming code is named for R.W Hamming worked at bell labs in 1940, it is a linear code for error detection and correction .

The subject of error-correcting codes was originally derived in response to practical problems in the reliable communication of digitally encoded information.

Communication channels where error-correcting codes are used, are too numerous to mention. Errors arise from a variety of causes some which are human, equipment failure, lighting, interference, or scratches on discs
How it's constructed
Briefly, a Hamming code is a binary code constructed from data bits interrupted by parity bits at every 2n position. Parity bits are used for checksum function over different subsets of the data bits, allowing the identification of substitution errors
Error detection and correction

Generalized DNA Barcode.

(16,8) Error correcting code (T=2) for critical memory applications.

Belief Propagation in Graphs with Cycles.

What is hamming code
How it can be constructed
Generalized DNA Barcode based on hamming code
What is barcoding
The need of hamming codes in the process of deep multiplex

Made by:
Aya Abo-Hagag
Yosra Ibrahim
Nada Alshaer

Hamming codes

Generalized DNA Barcode based on hamming code
R.W Hamming
Hamming used a rather elaborate checksum scheme: the 1st parity bit checks every odd position of the code word starting from the 1st position, the second parity bit checks consecutive pairs of bits starting with the 2nd position and interval of 2 bits, the 3rd bit will check 4 bits in a row starting from position 4 and interval 4, and so on
What is barcoding
Using a short genetic marker in an organism's DNA to identify to which a particular species it belongs is a taxonomic method which is called DNA barcoding
Deep Multiplex Process
Every DNA molecule consists of four amino acids A,C,G,T; every symbol can be encoded as a binary word its length is two bits.
For example “A” will be encoded as 00, “C” will be encoded as 01, “G” as 10, and “T” as 11. This is the conversion scheme of hamming codes, which will be translated into a sequence by converting each two bits into the quaternary DNA code.

So, it is clear that classical Hamming code adapted to the quaternary coding format is such a great accurate efficient tool to generate barcodes for multiplex sequencing applications. As hamming codes are sensitive to insertion/deletion transformation and cannot be corrected with previous algorithm. A positive point of using linear codes is in its simplicity as well as coding capacity, which is way more suitable and better than codes that are capable of correcting single indels.
let's say we have a message of 0110 and we need to construct a (7,4) code
so that means there are 3 parity bits
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