How Parity Detect Error

News Summary from the US/International Press on the Libyan Crisis - by Morgan ...

Retreat for Rebels; Libyan Foreign Minister Quits

( Washington Post ) - Libya’s foreign minister defected to Britain on Wednesday, dealing a blow to Col. Muammar Al Qathafi’s government even as his forces pushed rebels into a panicked retreat and seized valuable towns they ceded just days ago under allied airstrikes.

The government advance appeared to return control of eastern Libya’s most important oil regions to Colonel Al Qathafi’s forces, giving the isolated government, at least for the day, the east’s most valuable economic prize.

The rout also put into sharp relief the rebels’ absence of discipline and tactical sense, confronting the United States with a conundrum: how to persuade Colonel Al Qathafi to step down while supporting a rebel force that has been unable to hold on to military gains.

But the defection of Mussa Kussa, the foreign minister, showed that at least one longtime confidant seemed to be calculating that Colonel Al Qathafi could not last.

The news of Mr. Kussa's defection sent shockwaves through Tripoli on Wednesday night after it was announced by the British government. Mr. Kussa had been a pillar of his government since the early days of the revolution, and previously led the fearsome intelligence unit.

Although American officials suspected him of responsibility for the bombing of Pan Am 103 over Lockerbie, Scotland, Mr. Kussa also played a major role in turning over nuclear equipment and designs to the United States and in negotiating Libya back into the good graces of Western governments.

Presumably, he is now in a position to talk about the structure of Mr. Al Qathafi’s remaining forces and loyalists. What is unclear is whether his defection will lead to others. “We think he could be the beginning of a stream of Libyans who think sticking with Al Qathafi is a losing game,” one senior American official said. “But we don’t know.”

Having abandoned Bin Jawad and the oil port of Ras Lanuf on Tuesday, the rebels fled helter-skelter before government shelling from another oil town, Brega, and stopped for the night at the strategic city of Ajdabiyah.

As the rebels retreated in disarray, a senior rebel officer, Col. Ahmed Omar Bani, pleaded for more weapons. He conceded that rebel fighters had “dissolved like snow in the sand” but framed the retreat as a “tactical withdrawal.

Full Reading : Error detecting and error correcting codes « Xtreem ...

This is a summary of this paper published by R.W.Hamming on the topic of error detection and correction.

Summary

Error correction / detection is achieved by adding redundancy to the data.  Redundancy may not be considered simple duplication of data.  This paper discusses sophisticated methods to add redundancy that will help efficiently achieve single-error detection / single-error correction / single-error correction plus double-error detection. Redundancy factor R is defined as the ratio of total number bits to the number of data bits (the remaining being the parity bits). Single error detection is achieved as follows.  For every N bits we take N-1 bits as data bits and 1 bit as parity bit.  The parity bit is computed as the XOR of all the data bits.  In other words, the N bits (data plus parity) when put together will always have even number of ON bits.  Error is said to have occurred when the number of ON bits is not even.  N should be selected in such a way where the probability of single bit errors is high and at the same time the probability of two bit errors is low since this approach won’t be able to detect two-bit errors. For single error correcting codes I highly recommend you go through the paper.  In short, for every M data bits, we maintain K parity bits where K is chosen such that 2^K >= M+K+1.  This effectively means that the K parity bits are capable of indicating either there is no error or there is a single bit error in one of the M+K bits.  So, there are effectively M+K+1 pieces of info that has to be conveyed by the K bits and for that reason the equation 2^K >= M+K+1 should hold good.  The bit ordering of parity and info bits are also significant.  The parity bits are placed at positions that are powers of 2 (i.e., 1, 2, 4, 8 etc.).  The data bits are interleaved in the remaining positions.  Note that in this context, I’m counting positions from number 1 and not from zero.  The parity bit at position 2^Y is computed by XORing the data bits at positions X where X bitwise-AND 2^Y is nonzero.  For e.g., the parity bit at position 1 is XOR of data bits at positions (3,4,7,9,11 etc.).  The parity bit at position 2 is XOR of data bits at positions (2,3,6,7,10,11 etc.).  The parity bit at position 4 is XOR of data bits at positions (4,5,6,7,12,13,14,15 etc.).  Error detection is done by comparing the parity bits with the corresponding data-bit XOR values.

Switching Theory

Since the total number of Is is still even, the parity bit in the first row does not detect error. However, the parity bits in the 3rd and 4th columns do ...

Data Communication

This parity check bit has the value 1 if the number of 1's in the bit ... code is measured by the probability that the system fails to detect an error. ...

Modern digital electronics

The parity check method can only detect error in the transmitted word at the receiving end. It can not locate the bit which has changed and, therefore, ...

Digital electronics, principles, devices and applications

2.6.1 Parity Code A parity bit is an extra bit added to a string of data bits in order to detect any error that might have crept into it while it was being ...

Data and computer communications, networking and internetworking

This method enables the parity of each character in the frame to be checked and hence is used to detect errors in a block of data. The error-detection ...