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Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
Parity check is the special case where n = k + 1.From a set of k values {}, a checksum is computed and appended to the k source values: + = =. The set of k + 1 values {} + is now consistent with regard to the checksum.
Computing the square root of 2 (which is roughly 1.41421) is a well-posed problem.Many algorithms solve this problem by starting with an initial approximation x 0 to , for instance x 0 = 1.4, and then computing improved guesses x 1, x 2, etc.
The forward–backward algorithm runs with time complexity () in space (), where is the length of the time sequence and is the number of symbols in the state alphabet. [1] The algorithm can also run in constant space with time complexity O ( S 2 T 2 ) {\displaystyle O(S^{2}T^{2})} by recomputing values at each step. [ 2 ]
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
Reverse accumulation is more efficient than forward accumulation for functions f : R n → R m with n ≫ m as only m sweeps are necessary, compared to n sweeps for forward accumulation. Backpropagation of errors in multilayer perceptrons, a technique used in machine learning , is a special case of reverse accumulation.
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
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