1,330 research outputs found
On the error probability of general tree and trellis codes with applications to sequential decoding
An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random binary tree codes is derived and shown to be independent of the length of the tree. An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n is derived which separates the effects of the tail length T and the memory length M of the code. It is shown that the bound is independent of the length L of the information sequence. This implication is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication and further suggest an empirical formula for the true undetected decoding error probability with sequential decoding
Some long, rate one-half, binary convolutional codes with an optimum distance profile and the systematic versus nonsystematic code question
A tabulation is given of long systematic and long quick-look-in (QLI) nonsystematic rate R = 1/2 binary convolutional codes with an optimum distance profile (ODP). These codes appear attractive for use with sequential decoders. Simulations for two of the new codes are reported and confirm Massey's conjecture that systematic and non-systematic codes of the same rate yield nearly identical computational and error probability performance with sequential decoding when the number of digits transmitted in the tail of the encoded frame is the same for both codes
Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding
We show how extra entanglement shared between sender and receiver reduces the
memory requirements for a general entanglement-assisted quantum convolutional
code. We construct quantum convolutional codes with good error-correcting
properties by exploiting the error-correcting properties of an arbitrary basic
set of Pauli generators. The main benefit of this particular construction is
that there is no need to increase the frame size of the code when extra shared
entanglement is available. Then there is no need to increase the memory
requirements or circuit complexity of the code because the frame size of the
code is directly related to these two code properties. Another benefit, similar
to results of previous work in entanglement-assisted convolutional coding, is
that we can import an arbitrary classical quaternary code for use as an
entanglement-assisted quantum convolutional code. The rate and error-correcting
properties of the imported classical code translate to the quantum code. We
provide an example that illustrates how to import a classical quaternary code
for use as an entanglement-assisted quantum convolutional code. We finally show
how to "piggyback" classical information to make use of the extra shared
entanglement in the code.Comment: 7 pages, 1 figure, accepted for publication in Physical Review
Coordinated design of coding and modulation systems
The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems
Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
We analyze the dynamics of the helical edge modes of a quantum spin Hall
state in the presence of a spatially non-uniform Rashba spin-orbit (SO)
interaction. A randomly fluctuating Rashba SO coupling is found to open a
scattering channel which causes localization of the edge modes for a weakly
screened electron-electron (e-e) interaction. A periodic modulation of the SO
coupling, with a wave number commensurate with the Fermi momentum, makes the
edge insulating already at intermediate strengths of the e-e interaction. We
discuss implications for experiments on edge state transport in a HgTe quantum
well.Comment: 4 pages, 2 figures; published versio
Energy Injection in GRB Afterglow Models
We extend the standard fireball model, widely used to interpret gamma-ray
burst (GRB) afterglow light curves, to include energy injections, and apply the
model to the afterglow light curves of GRB 990510, GRB 000301C and GRB 010222.
We show that discrete energy injections can cause temporal variations in the
optical light curves and present fits to the light curves of GRB 000301C as an
example. A continuous injection may be required to interpret other bursts such
as GRB 010222. The extended model accounts reasonably well for the observations
in all bands ranging from X-rays to radio wavelengths. In some cases, the radio
light curves indicate that additional model ingredients may be needed.Comment: Accepted for publication in the Astrophysical Journa
The Fine-Structure of the Net-Circular Polarization in a Sunspot Penumbra
We present novel evidence for a fine structure observed in the net-circular
polarization (NCP) of a sunspot penumbra based on spectropolarimetric
measurements utilizing the Zeeman sensitive FeI 630.2 nm line. For the first
time we detect a filamentary organized fine structure of the NCP on spatial
scales that are similar to the inhomogeneities found in the penumbral flow
field. We also observe an additional property of the visible NCP, a
zero-crossing of the NCP in the outer parts of the center-side penumbra, which
has not been recognized before. In order to interprete the observations we
solve the radiative transfer equations for polarized light in a model penumbra
with embedded magnetic flux tubes. We demonstrate that the observed
zero-crossing of the NCP can be explained by an increased magnetic field
strength inside magnetic flux tubes in the outer penumbra combined with a
decreased magnetic field strength in the background field. Our results strongly
support the concept of the uncombed penumbra
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