We present the detailed characterization of two extremely red submillimeter galaxies ( SMGs ) , ASXDF1100.053.1 and 231.1 , with the Atacama Large Millimeter/submillimeter Array ( ALMA ) and the Jansky Very Large Array ( VLA ) . These SMGs were selected originally using AzTEC at 1100 \mu m , and are observed by Herschel to be faint at 100–500 \mu m. Their ( sub ) millimeter colors are as red as – or redder – than known z \gtrsim 5 SMGs ; indeed , ASXDF1100.053.1 is redder than HFLS 3 , which lies at z = 6.3 . They are also faint and red in the near-/mid-infrared : \sim 1 \mu Jy at IRAC 4.5 \mu m and < 0.2 \mu Jy in the K _ { s } filter . These SMGs are also faint in the radio waveband , where F _ { 6 GHz } = 4.5 \mu Jy for ASXDF1100.053.1 and F _ { 1.4 GHz } = 28 \mu Jy for ASXDF1100.231.1 , suggestive of z = 6.5 ^ { +1.4 } _ { -1.1 } and z = 4.1 ^ { +0.6 } _ { -0.7 } for ASXDF1100.053.1 and 231.1 , respectively . ASXDF1100.231.1 has a flux excess in the 3.6- \mu m filter , probably due to H \alpha emission at z = 4 –5 . Derived properties of ASXDF1100.053.1 for z = 5.5 –7.5 and 231.1 for z = 3.5 –5.5 are as follows : their infrared luminosities are [ 6.5 - 7.4 ] \times 10 ^ { 12 } and [ 4.2 - 4.5 ] \times 10 ^ { 12 } { L _ { \odot } } ; their stellar masses are [ 0.9 - 2 ] \times 10 ^ { 11 } and [ 0.4 - 3 ] \times 10 ^ { 10 } { M _ { \odot } } ; their circularized half-light radii in the ALMA maps are \sim 1 and \lesssim 0.2 kpc ( \sim 2–3 kpc for 90 % of the total flux ) . Lastly , their surface infrared luminosity densities , \Sigma _ { IR } , are \sim 1 \times 10 ^ { 12 } and \gtrsim 1.5 \times 10 ^ { 13 } { L _ { \odot } } kpc ^ { -2 } , similar to values seen for local ( U ) LIRGs . These data suggest that ASXDF1100.053.1 and 231.1 are compact SMGs at z \gtrsim 4 and can plausibly evolve into z \gtrsim 3 compact quiescent galaxies .