19,478 research outputs found
Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels
We consider a windowed decoding scheme for LDPC convolutional codes that is
based on the belief-propagation (BP) algorithm. We discuss the advantages of
this decoding scheme and identify certain characteristics of LDPC convolutional
code ensembles that exhibit good performance with the windowed decoder. We will
consider the performance of these ensembles and codes over erasure channels
with and without memory. We show that the structure of LDPC convolutional code
ensembles is suitable to obtain performance close to the theoretical limits
over the memoryless erasure channel, both for the BP decoder and windowed
decoding. However, the same structure imposes limitations on the performance
over erasure channels with memory.Comment: 18 pages, 9 figures, accepted for publication in the IEEE
Transactions on Information Theor
LDPC Codes with Local and Global Decoding
This paper presents a theoretical study of a new type of LDPC codes motivated
by practical storage applications. LDPCL codes (suffix L represents locality)
are LDPC codes that can be decoded either as usual over the full code block, or
locally when a smaller sub-block is accessed (to reduce latency). LDPCL codes
are designed to maximize the error-correction performance vs. rate in the usual
(global) mode, while at the same time providing a certain performance in the
local mode. We develop a theoretical framework for the design of LDPCL codes.
Our results include a design tool to construct an LDPC code with two
data-protection levels: local and global. We derive theoretical results
supporting this tool and we show how to achieve capacity with it. A trade-off
between the gap to capacity and the number of full-block accesses is studied,
and a finite-length analysis of ML decoding is performed to exemplify a
trade-off between the locality capability and the full-block error-correcting
capability.Comment: 41 page
Low Density Lattice Codes
Low density lattice codes (LDLC) are novel lattice codes that can be decoded
efficiently and approach the capacity of the additive white Gaussian noise
(AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional
Euclidean space as a linear transformation of a corresponding integer message
vector b, i.e., x = Gb, where H, the inverse of G, is restricted to be sparse.
The fact that H is sparse is utilized to develop a linear-time iterative
decoding scheme which attains, as demonstrated by simulations, good error
performance within ~0.5dB from capacity at block length of n = 100,000 symbols.
The paper also discusses convergence results and implementation considerations.Comment: 24 pages, 4 figures. Submitted for publication in IEEE transactions
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