GA pilot reported an NMAC during final approach to PDK airport requiring evasive action.

Narrative

I approached PDK from the NE; and joined the right downwind for Runway 3R. I found that I had turned downwind a little too late at this point; and looking out my right window saw that assigned Runway 3R was about a quarter up from the strut of my aircraft - much closer than I should be.I started to turn a bit to the left to increase this distance; and then was cleared to land #2 behind traffic. When parallel to the runway numbers; Tower advised that the traffic to follow was over the numbers about to touch down; and that there was traffic also cleared to land on the parallel Runway 3L. I responded that I had visual of the traffic about to touch down that I was to follow. I did not see the parallel traffic at this time.As I was getting ready to turn base I noticed that I was still much closer than I should have been to the runway. I turned base with a plan to continue the turn to final to account for my close approach. When halfway through this turn I noticed that the traffic on final for the parallel runway was just ahead and to the right of me.For a brief moment I was unsure of what to do; as I did not want to continue straight which would put me against the traffic flow for 3L; and I was not sure if I could safely continue my turn to Runway 3R without getting dangerously close to the parallel traffic. I elected to perform a sharp left turn to ensure I could get behind conflicting traffic; then turned right to finish my turn onto final. By the time I had completed my right turn I was aligned with Runway 3L and directly behind the traffic. I turned right to align with Runway 3R; and landed with no other notable events.There was no communication about this incident from the conflicting traffic or ATC. I'm not sure if either of them saw what had happened. I do not believe that fatigue or other physiological effects played a role in this incident. Reflecting on this event I believe that this situation should have been prevented by requesting an extended downwind to correct my distance from the runway.