4,298 research outputs found
Concatenation of Error Avoiding with Error Correcting Quantum Codes for Correlated Noise Models
We study the performance of simple error correcting and error avoiding
quantum codes together with their concatenation for correlated noise models.
Specifically, we consider two error models: i) a bit-flip (phase-flip) noisy
Markovian memory channel (model I); ii) a memory channel defined as a memory
degree dependent linear combination of memoryless channels with Kraus
decompositions expressed solely in terms of tensor products of X-Pauli
(Z-Pauli) operators (model II). The performance of both the three-qubit bit
flip (phase flip) and the error avoiding codes suitable for the considered
error models is quantified in terms of the entanglement fidelity. We explicitly
show that while none of the two codes is effective in the extreme limit when
the other is, the three-qubit bit flip (phase flip) code still works for high
enough correlations in the errors, whereas the error avoiding code does not
work for small correlations. Finally, we consider the concatenation of such
codes for both error models and show that it is particularly advantageous for
model II in the regime of partial correlations.Comment: 16 pages, 3 figure
New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding
The universal secure network coding presented by Silva et al. realizes secure
and reliable transmission of a secret message over any underlying network code,
by using maximum rank distance codes. Inspired by their result, this paper
considers the secure network coding based on arbitrary linear codes, and
investigates its security performance and error correction capability that are
guaranteed independently of the underlying network code. The security
performance and error correction capability are said to be universal when they
are independent of underlying network codes. This paper introduces new code
parameters, the relative dimension/intersection profile (RDIP) and the relative
generalized rank weight (RGRW) of linear codes. We reveal that the universal
security performance and universal error correction capability of secure
network coding are expressed in terms of the RDIP and RGRW of linear codes. The
security and error correction of existing schemes are also analyzed as
applications of the RDIP and RGRW.Comment: IEEEtran.cls, 8 pages, no figure. To appear in Proc. 50th Annual
Allerton Conference on Communication, Control, and Computing (Allerton 2012).
Version 2 added an exact expression of the universal error correction
capability in terms of the relative generalized rank weigh
- …