4 research outputs found
Structured LDPC Codes from Permutation Matrices Free of Small Trapping Sets
This paper introduces a class of structured lowdensity parity-check (LDPC)
codes whose parity check matrices are arrays of permutation matrices. The
permutation matrices are obtained from Latin squares and form a finite field
under some matrix operations. They are chosen so that the Tanner graphs do not
contain subgraphs harmful to iterative decoding algorithms. The construction of
column-weight-three codes is presented. Although the codes are optimized for
the Gallager A/B algorithm over the binary symmetric channel (BSC), their error
performance is very good on the additive white Gaussian noise channel (AWGNC)
as well.Comment: 5 pages, 3 figures, submitted to ITW Dublin 201
LDPC Decoding with Limited-Precision Soft Information in Flash Memories
This paper investigates the application of low-density parity-check (LDPC)
codes to Flash memories. Multiple cell reads with distinct word-line voltages
provide limited-precision soft information for the LDPC decoder. The values of
the word-line voltages (also called reference voltages) are optimized by
maximizing the mutual information (MI) between the input and output of the
multiple-read channel. Constraining the maximum mutual-information (MMI)
quantization to enforce a constant-ratio constraint provides a significant
simplification with no noticeable loss in performance.
Our simulation results suggest that for a well-designed LDPC code, the
quantization that maximizes the mutual information will also minimize the frame
error rate. However, care must be taken to design the code to perform well in
the quantized channel. An LDPC code designed for a full-precision Gaussian
channel may perform poorly in the quantized setting. Our LDPC code designs
provide an example where quantization increases the importance of absorbing
sets thus changing how the LDPC code should be optimized.
Simulation results show that small increases in precision enable the LDPC
code to significantly outperform a BCH code with comparable rate and block
length (but without the benefit of the soft information) over a range of frame
error rates
The Cycle Consistency Matrix Approach to Absorbing Sets in Separable Circulant-Based LDPC Codes
For LDPC codes operating over additive white Gaussian noise channels and
decoded using message-passing decoders with limited precision, absorbing sets
have been shown to be a key factor in error floor behavior. Focusing on this
scenario, this paper introduces the cycle consistency matrix (CCM) as a
powerful analytical tool for characterizing and avoiding absorbing sets in
separable circulant-based (SCB) LDPC codes. SCB codes include a wide variety of
regular LDPC codes such as array-based LDPC codes as well as many common
quasi-cyclic codes. As a consequence of its cycle structure, each potential
absorbing set in an SCB LDPC code has a CCM, and an absorbing set can be
present in an SCB LDPC code only if the associated CCM has a nontrivial null
space.
CCM-based analysis can determine the multiplicity of an absorbing set in an
SCB code and CCM-based constructions avoid certain small absorbing sets
completely. While these techniques can be applied to an SCB code of any rate,
lower-rate SCB codes can usually avoid small absorbing sets because of their
higher variable node degree. This paper focuses attention on the high-rate
scenario in which the CCM constructions provide the most benefit. Simulation
results demonstrate that under limited-precision decoding the new codes have
steeper error-floor slopes and can provide one order of magnitude of
improvement in the low FER region
Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets
This paper is concerned with construction and structural analysis of both
cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three
parts. The first part shows that a cyclic code given by a parity-check matrix
in circulant form can be decomposed into descendant cyclic and quasi-cyclic
codes of various lengths and rates. Some fundamental structural properties of
these descendant codes are developed, including the characterizations of the
roots of the generator polynomial of a cyclic descendant code. The second part
of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be
derived from cyclic finite geometry LDPC codes using the results developed in
first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The
third part of the paper analyzes the trapping sets of regular LDPC codes whose
parity-check matrices satisfy a certain constraint on their rows and columns.
Several classes of finite geometry and finite field cyclic and quasi-cyclic
LDPC codes with large minimum weights are shown to have no harmful trapping
sets with size smaller than their minimum weights. Consequently, their
performance error-floors are dominated by their minimum weights.Comment: 70 pages, submitted to IEEE Transactions on Information Theor