We present two sequences of ensembles of non-systematic irregular repeat-accumulate codes which asymptotically (as their block length tends to infinity) achieve capacity on the bi...
In [6], Gallager introduces a family of codes based on sparse bipartite graphs, which he calls low-density parity-check codes. He suggests a natural decoding algorithm for these c...
Michael Luby, Michael Mitzenmacher, Mohammad Amin ...
Let G be a simple graph of order n with no isolated vertices and no isolated edges. For a positive integer w, an assignment f on G is a function f : E(G) {1, 2, . . . , w}. For a ...
It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by...