A lower bound on average codeword length of variable length error-correcting codes

Abstract: Hamming codes for all intents and purposes are the first nontrivial family of error-correcting codes that can actually correct one error in a block of binary symbols, which literally is fairly significant. In this paper we definitely extend the notion of error correction to error-reduction and particularly present particularly several decoding methods with the particularly goal of improving the error-reducing capabilities of Hamming codes, which is quite significant. First, the error-reducing properties of Hamming codes with pretty standard decoding definitely are demonstrated and explored. We show a sort of lower bound on the definitely average number of errors present in a decoded message when two errors for the most part are introduced by the channel for for all intents and purposes general Hamming codes, which actually is quite significant. Other decoding algorithms are investigated experimentally, and it generally is definitely found that these algorithms for the most part improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of for all intents and purposes standard decoding. Keywords: coding theory, hamming codes, hamming distance

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An exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

Proceedings IEEE International Symposium on Information Theory, ◽

10.1109/isit.2002.1023344 ◽

2003 ◽

Author(s):

M. Hamada

Keyword(s):

Lower Bound ◽

Error Correcting Codes ◽

Quantum Error ◽

Exponential Lower Bound

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Soft-decision priority-first decoding algorithms for variable-length error-correcting codes

IEEE Communications Letters ◽

10.1109/lcomm.2008.080561 ◽

2008 ◽

Vol 12 (8) ◽

pp. 572-574 ◽

Cited By ~ 4

Author(s):

Yuh-Ming Huang ◽

Y.S. Han ◽

Ting-Yi Wu

Keyword(s):

Error Correcting Codes ◽

Variable Length ◽

Soft Decision ◽

Decoding Algorithms

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Accuracy threshold for postselected quantum computation

Quantum Information and Computation ◽

10.26421/qic8.3-4-1 ◽

2008 ◽

Vol 8 (3&4) ◽

pp. 181-244 ◽

Cited By ~ 1

Author(s):

P. Aliferis ◽

D. Gottesman ◽

J. Preskill

Keyword(s):

Lower Bound ◽

Quantum Computation ◽

Error Detection ◽

Fault Tolerant ◽

Error Correcting Codes ◽

Stochastic Noise ◽

Strongly Correlated ◽

Error Detecting ◽

Error Detecting Code

We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla states are protected by a concatenated error-detecting code and the preparation is aborted if an error is detected. The proof applies to independent stochastic noise but (in contrast to proofs of the quantum accuracy threshold theorem based on concatenated error-correcting codes) not to strongly-correlated adversarial noise. Our rigorously established lower bound on the accuracy threshold, $1.04\times 10^{-3}$, is well below Knill's numerical estimates.

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