Why We Can Not Surpass Capacity: The Matching Condition

We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity the various components in an iterative coding system have to be perfectly matched. This generalizes the perfect matching condition which was previously known for the case of transmission over the binary erasure channel to the general class of binary-input memoryless output-symmetric channels. Potential applications of this perfect matching condition are the construction of capacity-achieving degree distributions and the determination of the number required iterations as a function of the multiplicative gap to capacity.Comment: 10 pages, 27 ps figures. Forty-third Allerton Conference on Communication, Control and Computing, invited pape

The Generalized Area Theorem and Some of its Consequences

There is a fundamental relationship between belief propagation and maximum a posteriori decoding. The case of transmission over the binary erasure channel was investigated in detail in a companion paper. This paper investigates the extension to general memoryless channels (paying special attention to the binary case). An area theorem for transmission over general memoryless channels is introduced and some of its many consequences are discussed. We show that this area theorem gives rise to an upper-bound on the maximum a posteriori threshold for sparse graph codes. In situations where this bound is tight, the extrinsic soft bit estimates delivered by the belief propagation decoder coincide with the correct a posteriori probabilities above the maximum a posteriori threshold. More generally, it is conjectured that the fundamental relationship between the maximum a posteriori and the belief propagation decoder which was observed for transmission over the binary erasure channel carries over to the general case. We finally demonstrate that in order for the design rate of an ensemble to approach the capacity under belief propagation decoding the component codes have to be perfectly matched, a statement which is well known for the special case of transmission over the binary erasure channel.Comment: 27 pages, 46 ps figure

Anharmonic phonons in few layer MoS2_2: Raman spectroscopy of ultra low energy compression and shear modes

Molybdenum disulfide (MoS$_2$) is a promising material for making two-dimensional crystals and flexible electronic and optoelectronic devices at the nanoscale. MoS$_2$ flakes can show high mobilities and have even been integrated in nanocircuits . A fundamental requirement for such use is efficient thermal transport. Electronic transport generates heat which needs to be evacuated, more crucially so in nanostructures. Anharmonic phonon-phonon scattering is the dominant intrinsic limitation to thermal transport in insulators. Here, using appropriate samples, ultra-low energy Raman spectroscopy and first principles calculations, we provide a full experimental and theoretical description of compression and shear modes of few-layer (FL) MoS$_2$. We demonstrate that the compression modes are strongly anharmonic with a marked enhancement of phonon-phonon scattering as the number of layers is reduced, most likely a general feature of nanolayered materials with weak interlayer coupling.Comment: 6 pages, 5 figure

Magnetic transitions in CaMn7O12 : a Raman observation of spin-phonon couplings

The quadruple Calcium manganite (CaMn7O12) is a multiferroic material that exhibits a giant magnetically-induced ferroelectric polarization which makes it very interesting for magnetoelectric applications. Here, we report the Raman spectroscopy study on this compound of both the phonon modes and the low energy excitations from 4 K to room temperature. A detailed study of the Raman active phonon excitations shows that three phonon modes evidence a spin-phonon coupling at TN2 = 50 K. In particular, we show that the mode at 432 cm-1 associated to Mn(B)O6 (B position of the perovskite) rotations around the [111] cubic diagonal is impacted by the magnetic transition at 50 K and its coupling to the new modulation of the Mn spin in the (a,b) plane. At low energies, two large low energy excitations are observed at 25 and 47 cm-1. The first one disappears at 50 K and the second one at 90 K. We have associated these excitations to electro-magneto-active modes