Concatenated structure of left dihedral codes

Concatenated codes

Serially Concatenated IRA Codes

We address the error floor problem of low-density parity check (LDPC) codes on the binary-input additive white Gaussian noise (AWGN) channel, by constructing a serially concatenated code consisting of two systematic irregular repeataccumulate (IRA) component codes connected by an interleaver. The interleaver is designed to prevent stopping-set error events in one of the IRA codes from propagati...

Generalized concatenated quantum codes

Markus Grassl, Peter Shor, Graeme Smith, John Smolin, and Bei Zeng Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA Department of Physics, Massa...

Concatenated Conjugate Codes

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum code. It is known that conjugate code pairs are applicable to (quantum) cryptography. We give a construction method for efficiently decodable conjugate code pairs.

Concatenated codes with convolutional inner codes

We study the minimum distance of concatenated codes with Reed-Solomon outer codes and convolutional inner codes. For suitable combinations of parameters the minimum distance may be lower-bounded by the product of the minimum distances of the inner and outer codes. For a randomized ensemble of concatenated codes we prove a GilbertVarsharnov-type lower bound.