The iterative decoding algorithm used, the sumproduct algorithm, requires time proportional to the number of one bits in the parity check matrix times the number of iterations needed, which is generally fixed at some maximum, e.g. 20, after which the algorithm declares failure.
Current status of the DARPA Quantum Network
At present we fix the density so that each data bit is involved in an average of 5 parity checks; as a result, the density need not be sent to the other party.
Current status of the DARPA Quantum Network
This matrix can be expressed in an equivalent form by a bipartite graph G whose variable nodes (appearing on the left of G ) represent the the code bits, and whose parity-check nodes (appearing on the right of G ) represent the linear constraints deﬁned by H .
On Achievable Rates and Complexity of LDPC Codes for Parallel Channels with Application to Puncturing
So the task is essentially how to decide if |x| = k eﬃciently if we can query the XOR of arbitrary subsets of the bits of x.1 It is easy to see that deciding if the size of a parity is k is the same problem as deciding if it is n − k .
The non-adaptive query complexity of testing k-parities
In particular, in , the authors propose coding schemes, where, for every block of information packets, parity packets are transmitted such that ∀i, the ith bit from each packet arranged in sequence forms a codeword from an erasure correcting codebook.
Anonymous Networking amidst Eavesdroppers
As a ﬁrst task we have chosen the calculation of the parity of a binary string of n bits.
Insights into classical irreversible computation using quantum information concepts
Each user sends its own parity bits in the second frame.
Low-Density Graph Codes for slow fading Relay Channels
Symbols are split into three classes: i for the information bits, 1p and 2p for two classes of parity bits.
Low-Density Graph Codes for slow fading Relay Channels
Parity bits 2p are transmitted in the second frame, for example by the relay after successful decoding of the ﬁrst frame.
Low-Density Graph Codes for slow fading Relay Channels
As with standard LDPC encoding, these matrices will then be systemized to determine the parity bits.
Low-Density Graph Codes for slow fading Relay Channels
Symbols are split into three classes: i for the information bits, 1p and 2p for two classes of parity bits.
Low-Density Graph Codes for slow fading Relay Channels
Parity bits 2p are transmitted in the second frame, for example by the relay after successful decoding of the ﬁrst frame.
Low-Density Graph Codes for slow fading Relay Channels
The parity bits generated by the relay provide an extra protection through the code H2 .
Low-Density Graph Codes for slow fading Relay Channels
We report an inter-comparison of some popular algorithms within the artiﬁcial neural network domain ( viz., Local search algorithms, global search algorithms, higher order algorithms and the hybrid algorithms) by applying them to the standard benchmarking problems like the IRIS data, XOR/N-Bit parity and Two Spiral.
Comparative performance of some popular ANN algorithms on benchmark and function approximation problems
Our results suggest that while Levenberg-Marquardt algorithm yields the lowest RMS error for the N-bit Parity and the Two Spiral problems, Higher Order Neurons algorithm gives the best results for the IRIS data problem.
Comparative performance of some popular ANN algorithms on benchmark and function approximation problems
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