I. INTRODUCTION Recent analysis on the knowledge of neutrino oscillation parameters, which makes de- sirable a neutrino texture going beyond the mere fitting procedure, has shown in Table-I, which at 3 σ fully compatible with the TBM pattern Δ m 2 $_{Sol}$/ 10 − 5 eV 2 sin 2 θ$_{12}$ | U$_{e}$$_{3}$ | sin 2 θ$_{23}$ Δ m 2 $_{Atm}$/ 10 − 3 eV 2 Best-fit 7.67 0.312 0.126 0.466 2.39 1 σ 7 . 48 − 7 . 83 0 . 294 − 0 . 331 0 . 077 − 0 . 161 0 . 408 − 0 . 539 2 . 31 − 2 . 50 3 σ 7 . 14 − 8 . 19 0 . 263 − 0 . 375 < 0 . 214 0 . 331 − 0 . 644 2 . 06 − 2 . 81 TABLE I: Current best-fit values as well as 1 and 3 σ ranges of the oscillation parameters [1]. sin θ$_{12}$ = 1 √$_{3}$ , sin θ$_{23}$ = − 1 √$_{2}$ , sin θ$_{13}$ = 0 . (1) However, the recent analysis based on global fits of the available data gives us hints for θ$_{13}$ > 0 at 1 σ [2, 3]. Although neutrinos have gradually revealed their properties in various experiments since the historic Super-Kamiokande confirmation of neutrino oscillations [4], properties related to the leptonic CP violation are completely unknown yet. In addition, the large mixing values of θ$_{sol}$ ≡ θ$_{12}$ and θ$_{atm}$ ≡ θ$_{23}$ may be telling us about some new symmetries of leptons that are not present in the quark sector and may provide a clue of the nature among quark-lepton physics beyond the standard model. The most popular discrete symmetry µ − τ symmetry have some success in describing the mass and mixing pattern in the leptonic sector [5]. Nevertheless, E.Ma and G.Rajasekaran [6] have introduced for the first time the A$_{4}$ symmetry to avoid mass degeneracy of µ and τ under µ − τ symmetry. In a well- motivated extension of the standard model through the inclusion of A$_{4}$ discrete symmetry the TBM pattern comes out in a natural way in the work of [7]. Models of A$_{4}$ symmetry implemented with grand unification [8], supersymmetry [9], and extra dimensions[10, 11] are also investigated extensively in literatures. On the other hand, the observed baryon asymmetry in our universe (BAU) can be ex- plained by the mechanism of leptogenesis[12, 13]. A$_{4}$ models realized on type-I seesaw lead to vanishing leptonic CP-asymmetries responsible for leptogenesis due to the combination of Dirac neutrino Yukawa coupling matrix Y † ν Y$_{ν}$ being proportional to the unit matrix. A 2