276 research outputs found
High-Girth Matrices and Polarization
The girth of a matrix is the least number of linearly dependent columns, in
contrast to the rank which is the largest number of linearly independent
columns. This paper considers the construction of {\it high-girth} matrices,
whose probabilistic girth is close to its rank. Random matrices can be used to
show the existence of high-girth matrices with constant relative rank, but the
construction is non-explicit. This paper uses a polar-like construction to
obtain a deterministic and efficient construction of high-girth matrices for
arbitrary fields and relative ranks. Applications to coding and sparse recovery
are discussed
Deterministic Constructions for Large Girth Protograph LDPC Codes
The bit-error threshold of the standard ensemble of Low Density Parity Check
(LDPC) codes is known to be close to capacity, if there is a non-zero fraction
of degree-two bit nodes. However, the degree-two bit nodes preclude the
possibility of a block-error threshold. Interestingly, LDPC codes constructed
using protographs allow the possibility of having both degree-two bit nodes and
a block-error threshold. In this paper, we analyze density evolution for
protograph LDPC codes over the binary erasure channel and show that their
bit-error probability decreases double exponentially with the number of
iterations when the erasure probability is below the bit-error threshold and
long chain of degree-two variable nodes are avoided in the protograph. We
present deterministic constructions of such protograph LDPC codes with girth
logarithmic in blocklength, resulting in an exponential fall in bit-error
probability below the threshold. We provide optimized protographs, whose
block-error thresholds are better than that of the standard ensemble with
minimum bit-node degree three. These protograph LDPC codes are theoretically of
great interest, and have applications, for instance, in coding with strong
secrecy over wiretap channels.Comment: 5 pages, 2 figures; To appear in ISIT 2013; Minor changes in
presentatio
Polarization of the Renyi Information Dimension with Applications to Compressed Sensing
In this paper, we show that the Hadamard matrix acts as an extractor over the
reals of the Renyi information dimension (RID), in an analogous way to how it
acts as an extractor of the discrete entropy over finite fields. More
precisely, we prove that the RID of an i.i.d. sequence of mixture random
variables polarizes to the extremal values of 0 and 1 (corresponding to
discrete and continuous distributions) when transformed by a Hadamard matrix.
Further, we prove that the polarization pattern of the RID admits a closed form
expression and follows exactly the Binary Erasure Channel (BEC) polarization
pattern in the discrete setting. We also extend the results from the single- to
the multi-terminal setting, obtaining a Slepian-Wolf counterpart of the RID
polarization. We discuss applications of the RID polarization to Compressed
Sensing of i.i.d. sources. In particular, we use the RID polarization to
construct a family of deterministic -valued sensing matrices for
Compressed Sensing. We run numerical simulations to compare the performance of
the resulting matrices with that of random Gaussian and random Hadamard
matrices. The results indicate that the proposed matrices afford competitive
performances while being explicitly constructed.Comment: 12 pages, 2 figure
Heavy Squarks at the LHC
The LHC, with its seven-fold increase in energy over the Tevatron, is capable
of probing regions of SUSY parameter space exhibiting qualitatively new
collider phenomenology. Here we investigate one such region in which first
generation squarks are very heavy compared to the other superpartners. We find
that the production of these squarks, which is dominantly associative, only
becomes rate-limited at mSquark > 4(5) TeV for L~10(100) fb-1. However,
discovery of this scenario is complicated because heavy squarks decay primarily
into a jet and boosted gluino, yielding a dijet-like topology with missing
energy (MET) pointing along the direction of the second hardest jet. The result
is that many signal events are removed by standard jet/MET anti-alignment cuts
designed to guard against jet mismeasurement errors. We suggest replacing these
anti-alignment cuts with a measurement of jet substructure that can
significantly extend the reach of this channel while still removing much of the
background. We study a selection of benchmark points in detail, demonstrating
that mSquark= 4(5) TeV first generation squarks can be discovered at the LHC
with L~10(100)fb-1
Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?
In this paper, we highlight the class of spatially coupled codes and discuss
their applicability to long-haul and submarine optical communication systems.
We first demonstrate how to optimize irregular spatially coupled LDPC codes for
their use in optical communications with limited decoding hardware complexity
and then present simulation results with an FPGA-based decoder where we show
that very low error rates can be achieved and that conventional block-based
LDPC codes can be outperformed. In the second part of the paper, we focus on
the combination of spatially coupled LDPC codes with different demodulators and
detectors, important for future systems with adaptive modulation and for
varying channel characteristics. We demonstrate that SC codes can be employed
as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal
Processing, Coding, and Information Theory for Optical Communications" at
IEEE SPAWC 201
Comparison of different coding schemes for 1-bit ADC
This paper devotes to comparison of different coding schemes (various
constructions of Polar and LDPC codes, Product codes and BCH codes) for the
case when information is transmitted over AWGN channel with quantization with
lowest possible complexity and resolution: 1-bit. We examine performance (in
terms of Frame-error-rate -- FER) for schemes mentioned above and give some
reasoning for results we obtained. Also we give some recommendations for
choosing coding schemes for a given code rate and code length
Polar Coding Schemes for Cooperative Transmission Systems
: In this thesis, a serially-concatenated coding scheme with a polar code as the outer code and a low density generator matrix (LDGM) code as the inner code is firstly proposed. It is shown that that the proposed scheme provides a method to improve significantly the low convergence of polar codes and the high error floor of LDGM codes while keeping the advantages of both such as the low encoding and decoding complexity. The bit error rate results show that the proposed scheme by reasonable design have the potential to approach a performance close to the capacity limit and avoid error floor effectively. Secondly, a novel transmission protocol based on polar coding is proposed for the degraded half-duplex relay channel. In the proposed protocol, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. It is proved that the scheme can achieve the capacity of the half-duplex relay channel while enjoying low encoding/decoding complexity. By modeling the practical system, we verify that the proposed scheme outperforms the conventional scheme designed by low-density parity-check codes by simulations. Finally, a generalized partial information relaying protocol is proposed for degraded multiple-relay networks with orthogonal receiver components (MRN-ORCs). In such a protocol, each relay node decodes the received source message with the help of partial information from previous nodes and re-encodes part of the decoded message for transmission to satisfy the decoding requirements for the following relay node or the destination node. For the design of polar codes, the nested structures are constructed based on this protocol and the information sets corresponding to the partial messages forwarded are also calculated. It is proved that the proposed scheme achieves the theoretical capacity of the degraded MRN-ORCs while still retains the low-complexity feature of polar codes
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