Focus of this letter is the oldest class of codes that can approach the Shannon limit quite closely, i.e., lowdensity parity-check (LDPC) codes, and two mathematical tools that can make their design an easier job under appropriate assumptions. In particular, we present a simple algorithmic method to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output AWGN channels with sum-product decoding, and, to determine how close are the obtained thresholds to the theoretical maximum, i.e., to the Shannon limit, we give a simple and invertible expression of the AWGN channel capacity in the binary input - soft output case. For these codes, the thresholds are defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We assume a Gaussian approximation for message densities under density evolution, a widely used simplification of the decoding algorithm.

Useful Mathematical Tools for Capacity Approaching Codes Design

Babich, Fulvio;Soranzo, Alessandro;Vatta, Francesca
2017-01-01

Abstract

Focus of this letter is the oldest class of codes that can approach the Shannon limit quite closely, i.e., lowdensity parity-check (LDPC) codes, and two mathematical tools that can make their design an easier job under appropriate assumptions. In particular, we present a simple algorithmic method to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output AWGN channels with sum-product decoding, and, to determine how close are the obtained thresholds to the theoretical maximum, i.e., to the Shannon limit, we give a simple and invertible expression of the AWGN channel capacity in the binary input - soft output case. For these codes, the thresholds are defined as the maximum noise level such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We assume a Gaussian approximation for message densities under density evolution, a widely used simplification of the decoding algorithm.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2914303
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