Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs

Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs

A new technique, based on the pseudo-random properties of certain graphs, known as expanders, is used to obtain new simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling and then regrouping the code coordinates. For any fixed (small) rate, and for sufficiently large alphabet, the codes ...

Asymptotically Good Low-Rate Error-Correcting Codes through Pseudo-Random Graphs

A new technique, based on the pseudo-random properties of certain graphs, known as expanders, is used to obtain new simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling and then regrouping the code coordinates. For any fixed (small) rate, and for sufficiently large alphabet, the codes ...

Faster construction of asymptotically good unit-cost error correcting codes in the RAM model

Assuming we are in a Word-RAM model with word size w, we show that we can construct in o(w) time an error correcting code with a constant relative positive distance that maps numbers of w bits into Θ(w)-bit numbers, and such that the application of the error-correcting code on any given number x ∈ [0, 2w − 1] takes constant time. Our result improves on a previously proposed error-correcting cod...

Good Quantum Error-Correcting Codes based on Sparse Graphs

A construction technique for random-error-correcting convolutional codes