4,168 research outputs found
Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions
This paper examines the construction of low-density parity-check (LDPC) codes
from transversal designs based on sets of mutually orthogonal Latin squares
(MOLS). By transferring the concept of configurations in combinatorial designs
to the level of Latin squares, we thoroughly investigate the occurrence and
avoidance of stopping sets for the arising codes. Stopping sets are known to
determine the decoding performance over the binary erasure channel and should
be avoided for small sizes. Based on large sets of simple-structured MOLS, we
derive powerful constraints for the choice of suitable subsets, leading to
improved stopping set distributions for the corresponding codes. We focus on
LDPC codes with column weight 4, but the results are also applicable for the
construction of codes with higher column weights. Finally, we show that a
subclass of the presented codes has quasi-cyclic structure which allows
low-complexity encoding.Comment: 11 pages; to appear in "IEEE Transactions on Communications
Invertible Bloom Lookup Tables with Listing Guarantees
The Invertible Bloom Lookup Table (IBLT) is a probabilistic concise data
structure for set representation that supports a listing operation as the
recovery of the elements in the represented set. Its applications can be found
in network synchronization and traffic monitoring as well as in
error-correction codes. IBLT can list its elements with probability affected by
the size of the allocated memory and the size of the represented set, such that
it can fail with small probability even for relatively small sets. While
previous works only studied the failure probability of IBLT, this work
initiates the worst case analysis of IBLT that guarantees successful listing
for all sets of a certain size. The worst case study is important since the
failure of IBLT imposes high overhead. We describe a novel approach that
guarantees successful listing when the set satisfies a tunable upper bound on
its size. To allow that, we develop multiple constructions that are based on
various coding techniques such as stopping sets and the stopping redundancy of
error-correcting codes, Steiner systems, and covering arrays as well as new
methodologies we develop. We analyze the sizes of IBLTs with listing guarantees
obtained by the various methods as well as their mapping memory consumption.
Lastly, we study lower bounds on the achievable sizes of IBLT with listing
guarantees and verify the results in the paper by simulations
New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes
This paper presents several new construction techniques for low-density
parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on
specific classes of combinatorial designs, the improved code design focuses on
high-rate structured codes with constant column weights 3 and higher. The
proposed codes are efficiently encodable and exhibit good structural
properties. Experimental results on decoding performance with the sum-product
algorithm show that the novel codes offer substantial practical application
potential, for instance, in high-speed applications in magnetic recording and
optical communications channels.Comment: 10 pages; to appear in "IEEE Transactions on Communications
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