Is something like this what you’re looking for?

#! perl
use strict;
use warnings;
use JSON;

my @fields = qw(eTime lTime eCompressd eUnCompressd iCompressd iUnComp
+ressd);
my $j = JSON->new;

{
    local $/ = '}';

    while (my $jsonstr = <DATA>)
    {
        my $structure = $j->decode($jsonstr);
        print "\n========== RECORD ===========\n\n";
        printf("%-12s = %s\n", $_, $structure->{$_}) for @fields;
    }
}

__DATA__
<as before>
[download]

Output:

19:36 >perl 854_SoPW.pl

========== RECORD ===========

eTime        = 1390798621000
lTime        = 1390802201000
eCompressd   = 22627786
eUnCompressd = 31929200
iCompressd   = 255554
iUnCompressd = 643408

========== RECORD ===========

eTime        = 1390802241000
lTime        = 1390805821000
eCompressd   = 21470491
eUnCompressd = 29827772
iCompressd   = 253899
iUnCompressd = 637636

========== RECORD ===========

eTime        = 1390805861000
lTime        = 1390809441000
eCompressd   = 16216565
eUnCompressd = 27731136
iCompressd   = 233005
iUnCompressd = 639488

19:36 >
[download]

Notes:

1. The OP code reads only the first record, as it calls <DATA> only once.
2. For efficiency, put things that aren’t changed by the loop outside of it.

Hope that helps,