40 research outputs found
Punctured Binary Simplex Codes as LDPC codes
Digital data transfer can be protected by means of suitable error correcting
codes. Among the families of state-of-the-art codes, LDPC (Low Density
Parity-Check) codes have received a great deal of attention recently, because
of their performance and flexibility of operation, in wireless and mobile radio
channels, as well as in cable transmission systems. In this paper, we present a
class of rate-adaptive LDPC codes, obtained as properly punctured simplex
codes. These codes allow for the use of an efficient soft-decision decoding
algorithm, provided that a condition called row-column constraint is satisfied.
This condition is tested on small-length codes, and then extended to
medium-length codes. The puncturing operations we apply do not influence the
satisfaction of the row-column constraint, assuring that a wide range of code
rates can be obtained. We can reach code rates remarkably higher than those
obtainable by the original simplex code, and the price in terms of minimum
distance turns out to be relatively small, leading to interesting trade-offs in
the resulting asymptotic coding gain
Time-Invariant Spatially Coupled Low-Density Parity-Check Codes with Small Constraint Length
We consider a special family of SC-LDPC codes, that is, time-invariant LDPCC
codes, which are known in the literature for a long time. Codes of this kind
are usually designed by starting from QC block codes, and applying suitable
unwrapping procedures. We show that, by directly designing the LDPCC code
syndrome former matrix without the constraints of the underlying QC block code,
it is possible to achieve smaller constraint lengths with respect to the best
solutions available in the literature. We also find theoretical lower bounds on
the syndrome former constraint length for codes with a specified minimum length
of the local cycles in their Tanner graphs. For this purpose, we exploit a new
approach based on a numerical representation of the syndrome former matrix,
which generalizes over a technique we already used to study a special subclass
of the codes here considered.Comment: 5 pages, 4 figures, to be presented at IEEE BlackSeaCom 201
Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length
In this paper, we deal with time-invariant spatially coupled low-density
parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches
usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes
and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that
the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently,
the symbolic parity-check matrix, leads to codes with smaller syndrome former
constraint lengths with respect to the best solutions available in the
literature. We provide theoretical lower bounds on the syndrome former
constraint length for the most relevant families of SC-LDPC-CCs, under
constraints on the minimum length of cycles in their Tanner graphs. We also
propose new code design techniques that approach or achieve such theoretical
limits.Comment: 30 pages, 5 figures, accepted for publication in IEEE Transactions on
Communication
Compact QC-LDPC Block and SC-LDPC Convolutional Codes for Low-Latency Communications
Low decoding latency and complexity are two important requirements of channel
codes used in many applications, like machine-to-machine communications. In
this paper, we show how these requirements can be fulfilled by using some
special quasi-cyclic low-density parity-check block codes and spatially coupled
low-density parity-check convolutional codes that we denote as compact. They
are defined by parity-check matrices designed according to a recent approach
based on sequentially multiplied columns. This method allows obtaining codes
with girth up to 12. Many numerical examples of practical codes are provided.Comment: 5 pages, 1 figure, presented at IEEE PIMRC 201
Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes with Large Girth
We propose a low-complexity method to find quasi-cyclic low-density
parity-check block codes with girth 10 or 12 and shorter length than those
designed through classical approaches. The method is extended to time-invariant
spatially coupled low-density parity-check convolutional codes, permitting to
achieve small syndrome former constraint lengths. Several numerical examples
are given to show its effectiveness.Comment: 4 pages, 3 figures, 1 table, accepted for publication in IEEE
Communications Letter
Rate-compatible LDPC Codes based on Primitive Polynomials and Golomb Rulers
We introduce and study a family of rate-compatible Low-Density Parity-Check
(LDPC) codes characterized by very simple encoders. The design of these codes
starts from simplex codes, which are defined by parity-check matrices having a
straightforward form stemming from the coefficients of a primitive polynomial.
For this reason, we call the new codes Primitive Rate-Compatible LDPC
(PRC-LDPC) codes. By applying puncturing to these codes, we obtain a bit-level
granularity of their code rates. We show that, in order to achieve good LDPC
codes, the underlying polynomials, besides being primitive, must meet some more
stringent conditions with respect to those of classical punctured simplex
codes. We leverage non-modular Golomb rulers to take the new requirements into
account. We characterize the minimum distance properties of PRC-LDPC codes, and
study and discuss their encoding and decoding complexity. Finally, we assess
their error rate performance under iterative decoding
Analysis of a Blockchain Protocol Based on LDPC Codes
In a blockchain Data Availability Attack (DAA), a malicious node publishes a block header but withholds part of the block, which contains invalid transactions. Honest full nodes, which can download and store the full ledger, are aware that some data are not available but they have no formal way to prove it to light nodes, i.e., nodes that have limited resources and are not able to access the whole blockchain data.
A common solution to counter these attacks exploits linear error correcting codes to encode the block content.
A recent protocol, called SPAR, employs coded Merkle trees and low-density parity-check codes to counter DAAs. In this paper, we show that the protocol is less secure than claimed, owing to a redefinition of the adversarial success probability. As a consequence we show that, for some realistic choices of the parameters, the total amount of data downloaded by light nodes is larger than that obtainable with competing solutions
Analysis of a blockchain protocol based on LDPC codes
In a blockchain Data Availability Attack (DAA), a malicious node publishes a
block header but withholds part of the block, which contains invalid
transactions. Honest full nodes, which can download and store the full
blockchain, are aware that some data are not available but they have no formal
way to prove it to light nodes, i.e., nodes that have limited resources and are
not able to access the whole blockchain data. A common solution to counter
these attacks exploits linear error correcting codes to encode the block
content. A recent protocol, called SPAR, employs coded Merkle trees and
low-density parity-check (LDPC) codes to counter DAAs. We show that the
protocol is less secure than expected, owing to a redefinition of the
adversarial success probability