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Slide_And_Increment(leaf node) sliding step 2. As P is leaf node, it slides in front of next block nodes of equal weight. Slide_And_Increment(leaf node) sliding step 3. Here we increase the current weight by 1. Slide_And_Increment(leaf node) sliding step 4. Method comes to an end. P is the new parent. Slide_And_Increment(internal node) sliding ...
Since the source is only 4 bits then there are only 16 possible transmitted words. Included is the eight-bit value if an extra parity bit is used (see Hamming(7,4) code with an additional parity bit).
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages.
The rate of a block code is defined as the ratio between its message length and its block length: = /. A large rate means that the amount of actual message per transmitted block is high.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
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Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code , with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).