THE PLT HAD JUST RTRND FM VACATION IN THE BAHAMAS BFR STARTING A FLT FM LITTLE ROCK TO ATLANTA WITH AN INTERMEDIATE STOPAT MEMPHIS. THIS ITINERARY WAS FLWD BY A RTRN FLT TO LITTLE ROCK VIA A REVERSE ROUTING. WITNESSES RPRTD THE PLT SAID HE HAD ONLY 2 HRS OF SLEEP BFR DEPG LITTLE ROCK & THAT HE WAS REALLY TIRED. ALSO, COMPANY PSNL NOTED THE PLT LOOKED 'EXTREMELY TIRED' & WAS 'REALLY DRAGGING' PRIOR TO THE LAST LEG OF THE FLT FM MEMPHIS TO LITTLE ROCK. ACCORDING TO ATC PSNL, THE FLT WAS ROUTINE UNTIL THE ACFT WAS ARRIVING AT LITTLE ROCK. DRG ARRIVAL, THE PLT WAS CLRD TO DSCND FM 7000' TO 2000' AT HIS DISCRETION FOR A VISUAL APCH TO RWY 22. AT 0522 CDT, THE PLT RPRTD THE ARPT IN SIGHT & WAS CLRD FOR A VISUAL APCH. ABT 4 MIN LATER, HE AGAIN RPRTD THE ARPT IN SIGHT & WAS CLRD TO LAND. AT 1031, RADAR CONTACT WAS LOST & THE ACFT CRASHED ABT 4 MI WEST OF THE ARPT. INITIAL IMPACT WAS IN AN OPEN FIELD WHILE DSCNDG IN A RELATIVELY LEVEL ATTITUDE. THE ACFT BCM AIRBORNE FOR ABOUT 3/4 MI, THEN CRASHED OUT OF CTL IN THE ARKANSAS RIVER.