Why is resolution 20? I am using an amazing code to send/read infrared pulses without any external library. The code is fine and I took about 1 hour to fully understand it. The only thing I didnt understand is the variable RESOLUTION. I believe it should be 0 not 20. I think it should be as low as possible.

You can see the code at:

https://learn.adafruit.com/ir-sensor/using-an-ir-sensor

or below:

/* Raw IR decoder sketch!
This sketch/program uses the Arduino and a PNA4602 to
decode IR received. This can be used to make a IR receiver
(by looking for a particular code)
or transmitter (by pulsing an IR LED at ~38KHz for the
durations detected
Code is public domain, check out www.ladyada.net and adafruit.com
for more tutorials!
*/

// We need to use the 'raw' pin reading methods
// because timing is very important here and the digitalRead()
// procedure is slower!
//uint8_t IRpin = 2;
// Digital pin #2 is the same as Pin D2 see
// http://arduino.cc/en/Hacking/PinMapping168 for the 'raw' pin mapping
#define IRpin_PIN PIND
#define IRpin 2
// for MEGA use these!
//#define IRpin_PIN PINE
//#define IRpin 4

// the maximum pulse we'll listen for - 65 milliseconds is a long time
#define MAXPULSE 65000

// what our timing resolution should be, larger is better
// as its more 'precise' - but too large and you wont get
// accurate timing
#define RESOLUTION 20

// we will store up to 100 pulse pairs (this is -a lot-)
uint16_t pulses[100][2]; // pair is high and low pulse
uint8_t currentpulse = 0; // index for pulses we're storing

void setup(void) {
  Serial.begin(9600);
  Serial.println("Ready to decode IR!");
}

void loop(void) {
  uint16_t highpulse, lowpulse; // temporary storage timing
  highpulse = lowpulse = 0; // start out with no pulse length


// while (digitalRead(IRpin)) { // this is too slow!
    while (IRpin_PIN &amp; (1 &lt;&lt; IRpin)) {
     // pin is still HIGH

     // count off another few microseconds
     highpulse++;
     delayMicroseconds(RESOLUTION);

     // If the pulse is too long, we 'timed out' - either nothing
     // was received or the code is finished, so print what
     // we've grabbed so far, and then reset
     if ((highpulse &gt;= MAXPULSE) &amp;&amp; (currentpulse != 0)) {
       printpulses();
       currentpulse=0;
       return;
     }
  }
  // we didn't time out so lets stash the reading
  pulses[currentpulse][0] = highpulse;

  // same as above
  while (! (IRpin_PIN &amp; _BV(IRpin))) {
     // pin is still LOW
     lowpulse++;
     delayMicroseconds(RESOLUTION);
     if ((lowpulse &gt;= MAXPULSE) &amp;&amp; (currentpulse != 0)) {
       printpulses();
       currentpulse=0;
       return;
     }
  }
  pulses[currentpulse][1] = lowpulse;

  // we read one high-low pulse successfully, continue!
  currentpulse++;
}

void printpulses(void) {
  Serial.println("\n\r\n\rReceived: \n\rOFF \tON");
  for (uint8_t i = 0; i &lt; currentpulse; i++) {
    Serial.print(pulses
* RESOLUTION, DEC);

    Serial.print(" usec, ");
    Serial.print(pulses[1] * RESOLUTION, DEC);
    Serial.println(" usec");
  }

  // print it in a 'array' format
  Serial.println("int IRsignal[] = {");
  Serial.println("// ON, OFF (in 10's of microseconds)");
  for (uint8_t i = 0; i &lt; currentpulse-1; i++) {
    Serial.print("\t"); // tab
    Serial.print(pulses[1] * RESOLUTION / 10, DEC);
    Serial.print(", ");
    Serial.print(pulses[i+1][0] * RESOLUTION / 10, DEC);
    Serial.println(",");
  }
  Serial.print("\t"); // tab
  Serial.print(pulses[currentpulse-1][1] * RESOLUTION / 10, DEC);
  Serial.print(", 0};");
}
Most IR remotes send pulses that are at least 400 micro seconds long. E.g. on a NEC IR remote you get pulses that are 560 or 2240 microseconds long (depending on whether it's sending a 1 or a 0). 

So with a RESOLUTION of 20 you get at least 20 'pulse counts' for a 0 and 80 for a 1. Because remotes aren't that precise in you'll get somewhere between e.g. 18 and 22 or 78 and 82. Those values are different enough to easily detect whether a 0 or 1 was send. 

Changing this RESOLUTION to e.g. 2 will give you 200 or 800 pulsecounts. You'll get a more precise timings from a still imprecise source. But this better precision is useless.

PS setting it to 0 could break the code, as the highpulse and lowpulse are only 16 bit integers so they will overflow after 65536, which will happen pretty fast.

Hope that helps somewhat. Just let me know is anything is still unclear.