Change the definition of "$/" about what a new line is, in this case, the records are separated on each empty line and no chomping's done hence the records structure is preserved for each line, however, you might wanna chop if you wanted to get rid of the trailing new line characters for each independent record..

use strict;
use warnings;

local $/='';      #Empty lines are the record terminators
while(<DATA>){
       # print if !/^r145/;
        print unless /^r145/;
        }
__DATA__
c114:   0245,   0456,   1545
        2555,    2444,    0344
        0444,    3434,    1434

r145:    0544,    0688,    2988
        1332,    0221,    0867
        0655,    4548,    7463

c12:    2322,    0556,    3998
        3545,    2002,    4500
        5650,    0830,    3324
        3433,    7070,    3404
[download]

OUTPUTS:

c114:   0245,   0456,   1545
        2555,    2444,    0344
        0444,    3434,    1434

c12:    2322,    0556,    3998
        3545,    2002,    4500
        5650,    0830,    3324
        3433,    7070,    3404
[download]