To　deal　with　random　communication　time-delays,　the　H-Infinity　filtering　problem　is　investigated　for　a　class　of　discrete-time　switched　systems　with　arbitrary　switching　laws.　The　delayed　data　packets　include　the　measured　output　and　the　switched　signal;　and　the　delay-time　satisfies　the　Bernoulli　random　binary　distribution.　By　using　the　switched　Lyapunov　function,　we　obtain　the　full　and　reduced-order　switched　filters.　The　systems　of　filtering　errors　are　exponentially　mean-square　stable　and　satisfy　the　prescribed　H-Infinity　performance　constraint.　The　filter　parameters　can　be　obtained　by　solving　a　set　of　linear　matrix　inequalities(LMIs).　Finally,　a　numerical　example　is　provided　to　illustrate　the　application　of　the　proposed　design　method.