Tag: error correction

More on parity matrices
Here’s a generator matrix, A parity check matrix for this, is one where (hence the product of with a codeword is also 0, though an error word generates a nonzero output). Two candidates for this present themselves (are there others? I can’t see them): Taking , there are distinct messages (codewords), where , but he…

Convolutional coding
Convolutional coding is form of errorcorrection widely used in mobile communications and is another area of life where discrete mathematics is hard at work for us, even though we are unlikely ever to think about it. The basic idea in convolutional coding are that a stream of bits of length is converted to a different…

Cartesian product or Kronecker product?
I am continuing to work my way through A. K. Dewdney‘s New Turing Omnibus – some bits are very familiar and not so interesting, but there are lots of fascinating parts and it is another book I wish I’d read two years ago, before I started the MSc. (Update: you may want to read this).…