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Serial concatenated convolutional codes; Shaping codes; Slepian–Wolf coding; Snake-in-the-box; Soft-decision decoder; Soft-in soft-out decoder; Sparse graph code; Srivastava code; Stop-and-wait ARQ; Summation check
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 ...
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 ()).
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
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.
LDPC codes functionally are defined by a sparse parity-check matrix. This sparse matrix is often randomly generated, subject to the sparsity constraints—LDPC code construction is discussed later. These codes were first designed by Robert Gallager in 1960. [5] Below is a graph fragment of an example LDPC code using Forney's factor graph notation.
Virtual Villagers is a series of village simulator video games created and developed by Last Day of Work, an independent video game developer and publisher.Each game contains puzzles the player must complete to uncover the ethnic and cultural backgrounds surrounding fictional Polynesian island called Isola (EE-zoh-la).
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).