Consumer　electronic　devices　often　involve　processing　and　analyzing　a　large　amount　of　user　personal　data.　Nevertheless,　owing　to　apprehensions　regarding　privacy　and　security,　users　are　hesitant　to　transmit　this　sensitive　data　to　centralized　cloud　servers　for　training.　The　combination　of　mobile　edge　computing　and　federated　learning　(FL)　enables　local　devices　to　access　computational　power　and　storage　resources,　allowing　them　to　engage　in　distributed　learning　and　model　training　while　safeguarding　user　privacy.　However,　these　resources　are　not　unlimited.　Furthermore,　as　artificial　intelligence　technology　progresses,　inference　attacks　have　become　a　major　threat　to　privacy　in　traditional　federated　learning.　To　address　these　challenges,　we　propose　an　innovative　federated　deep　learning　algorithm,　called　Fed-PEMC.　This　algorithm　combines　local　differential　privacy　and　model　compression　techniques.　By　leveraging　deep　reinforcement　learning　for　model　compression,　Fed-PEMC　reduces　model　size　while　maintaining　model　accuracy,　improving　communication　efficiency.　We　also　introduce　customized　label　sampling　to　accelerate　model　training.　Before　uploading　the　model,　we　implement　local　differential　privacy　protection　on　the　compressed　model,　reducing　privacy　budget　and　addressing　privacy　leakage　caused　by　inference　attacks.　Theoretical　analysis　and　experimental　results　validate　that　Fed-PEMC　adheres　to　(epsilon,　delta)　-differential　privacy　and　exhibits　a　communication　cost　linked　to　the　model　size.　Experimental　results　show　that　compared　to　baseline　algorithms,　Fed-PEMC　excels　in　ensuring　privacy,　maintaining　model　accuracy,　and　optimizing　communication　efficiency,　and　Fed-PEMC　outperforms　the　baseline　solution　DP-Fed　by　2.27　and　2.02　percentage　points　in　testing　accuracy　on　the　Mnist　and　Cifar10　datasets,　respectively.