A STUDENT PLT MISUNDERSTANDS THE ABBREVIATED SIMILAR CALL SIGN USED BY THE LCL CTLR TO ISSUE A GAR TO ANOTHER ACFT AS HIS CLRNC TO TAKE OFF AND ENTERS RWY 25L WITHOUT AUTH AT LGB.

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STUDENT PLT WAS SOLO IN CHEROKEE X AND WAS HOLDING SHORT OF RWY 25L AT INTXN D. HE OBSERVED ACFT Y LNDG. TWR WAS EXTREMELY BUSY; AND MANY CALLS WERE TAKING PLACE. ACFT Y WAS TAKING A LONG TIME FOR ITS 'TOUCH AND GO;' SO TWR INSTRUCTED 'ACFT Y IF YOU'RE GOING TO GO; GO NOW' TWR THEN TOLD LNDG TFC BEHIND; TO GO AROUND. STUDENT PLT MISHEARD THE CALL SIGN Y; AND THOUGHT THAT TWR WAS TELLING HIM TO 'GO NOW' AND SO HE STARTING ROLLING ONTO THE RWY AND REPLIED 'CHEROKEE X ROLLING; RWY 25L.' TWR CAME BACK AND INSTRUCTED STUDENT TO STOP IMMEDIATELY; EXIT THE RWY AND CALL THE TWR. NO OTHER ACFT WAS ON THE RWY; AND THE LNDG ACFT HAD ALREADY BEEN TOLD TO GO AROUND. UPON REFLECTION; STUDENT PLT INCORRECTLY THOUGHT HE HAD MISSED A TKOF CLRNC; AND THAT TWR WAS GETTING IMPATIENT WITH HIM. HE HAS RECEIVED ADDITIONAL TRAINING FROM HIS INSTRUCTOR; AND NOW UNDERSTANDS THAT HE MUST HEAR 'CLR FOR TKOF' OR 'POS AND HOLD' BEFORE HE CAN ENTER A RWY. FURTHERMORE; HE UNDERSTANDS THAT HE MUST BE MORE VIGILANT WHEN LISTENING TO TAIL NUMBERS AND OTHER CALLS; AND MAINTAIN BETTER SITUATIONAL AWARENESS.