  One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman
magnetic field is shown to lead to the formation of a helical charge-density
wave (CDW) state near half-filling. Interplay of the magnetic field, SOI
constants and the CDW gap seems to support Majorana bound states under
appropriate value of the external parameters. Explicit calculation of the
quasi-particles' wave functions supports a formation of the localized
zero-energy state, bounded to the sample end-points. Symmetry classification of
the system is provided. Relative value of the density of states shows a precise
zero-energy peak at the center of the band in the non-trivial topological
regime.
