Matrix analysis
Computer Methods for Circuit Analysis and Design
Computer Methods for Circuit Analysis and Design
A SiGe BiCMOS analog SISO decoder with I/O interface
Analog Integrated Circuits and Signal Processing
Dynamics of analog decoders for different message representation domains
IEEE Transactions on Communications
On the dynamics of the error floor behavior in (regular) LDPC codes
IEEE Transactions on Information Theory
Probability propagation and decoding in analog VLSI
IEEE Transactions on Information Theory
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In this paper, we show an ideal analog min-sum decoder, in the log-likelihood ratio domain, can be considered as a piecewise linear system. Many theoretical aspects of these decoders, thus, can be studied analytically. It is also shown that the dynamic equations can become singular for codes with cycles. When it is non-singular, the corresponding dynamic equations can be solved analytically to derive outputs of the decoder. We study the relationship between singularity and error floor and prove that absorption sets with degree two check nodes are singular graphs and under specific conditions the dynamic equations of an analog min-sum decoder can be reduced to that of an absorption set. The proposed approach paves the way for further analytical analysis on the dynamics of analog min-sum decoders and error floor in low-density parity-check codes.