Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cavity approach to the Sourlas code system   The statistical physics properties of regular and irregular Sourlas codes are
investigated in this paper by the cavity method. At finite temperatures, the
free energy density of these coding systems is derived and compared with the
result obtained by the replica method. In the zero temperature limit, the
Shannon's bound is recovered in the case of infinite-body interactions while
the code rate is still finite. However, the decoding performance as obtained by
the replica theory has not considered the zero-temperature entropic effect. The
cavity approach is able to consider the ground-state entropy. It leads to a set
of evanescent cavity fields propagation equations which further improve the
decoding performance, as confirmed by our numerical simulations on single
instances. For the irregular Sourlas code, we find that it takes the trade-off
between good dynamical property and high performance of decoding. In agreement
with the results found from the algorithmic point of view, the decoding
exhibits a first order phase transition as occurs in the regular code system
with three-body interactions. The cavity approach for the Sourlas code system
can be extended to consider first-step replica-symmetry-breaking.

33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat