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It includes the Zero Redundancy Optimizer (ZeRO) for training models with 1 trillion or more parameters. [4] Features include mixed precision training, single-GPU, multi-GPU, and multi-node training as well as custom model parallelism. The DeepSpeed source code is licensed under MIT License and available on GitHub. [5]
"Don't repeat yourself" (DRY), also known as "duplication is evil", is a principle of software development aimed at reducing repetition of information which is likely to change, replacing it with abstractions that are less likely to change, or using data normalization which avoids redundancy in the first place.
The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels. When the number of recursions becomes large, the virtual channels tend to either have high reliability or low reliability (in other words, they polarize or become sparse), and the data ...
The code-rate is hence a real number. A low code-rate close to zero implies a strong code that uses many redundant bits to achieve a good performance, while a large code-rate close to 1 implies a weak code. The redundant bits that protect the information have to be transferred using the same communication resources that they are trying to protect.
Note that this example code avoids the need to specify a bit-ordering convention by not using bytes; the input bitString is already in the form of a bit array, and the remainderPolynomial is manipulated in terms of polynomial operations; the multiplication by could be a left or right shift, and the addition of bitString[i+n] is done to the ...
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
These two variations serve the purpose of detecting zero bits added to the message. A preceding zero bit adds a leading zero coefficient to (), which does not change its value, and thus does not change its divisibility by the generator polynomial. By adding a fixed pattern to the first bits of a message, such extra zero bits can be detected.
For example, the widely used (255,223) code can be converted to a (160,128) code by padding the unused portion of the source block with 95 binary zeroes and not transmitting them. At the decoder, the same portion of the block is loaded locally with binary zeroes. The QR code, Ver 3 (29×29) uses interleaved blocks.