Methods for coding and decoding LDPC codes, and method for...

Error detection/correction and fault detection/recovery – Pulse or data error handling – Digital data error correction

Reexamination Certificate

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C714S801000

Reexamination Certificate

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07406648

ABSTRACT:
Provided are methods for encoding and decoding low-density parity-check (LDPC) codes and a method for forming an LDPC parity check matrix. The method for forming the LDPC parity check matrix, includes the steps of: preparing a plurality of parity check matrixes; and selecting a parity check matrix having maximum performance from the prepared parity check matrixes, wherein the parity check matrix has a degree distribution G(x) that meets an equation,G⁡(x)=∑k=2di-1⁢ak⁢xk+∑k=didmax⁢C⁢⁢k-γ⁢xk⁢⁢or⁢⁢G⁡(x)=⁢∑k=2dmax⁢C⁡(k+α)-γ⁢xk,where, akis a parameter that corresponds to the probability that nodes of the graph have a degree k, C is a parameter that is determined by a normalization condition, G(1)=1, and α, γ are parameters that is optimized through numerical calculations. This may significantly decrease a time to discover an optimal code by using a power-law distribution with less parameters in designing the LDPC codes, as compared with numerical optimization in a global parameter space.

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