TPL versus DPL

thgiz · Post by **thgiz** » Mon Oct 28, 2002 6:26 am

Which is better? TPL or DPL? i will be using maxtracs, visars, GP300s, HT1000s, HT750s, and M1225s on the systems so they all can do both. will be in the UHF band and on a repeater system (2 maxtracs and a rick) we currently use CSQ. Thanks

larryepage · Post by **larryepage** » Mon Oct 28, 2002 8:14 am

There are a large number of factors to consider when selecting DPL vs. TPL. I will give you one short answer based on my experience. Others will likely have different views...

The biggest advantage of DPL over TPL is that there are more different choices of codes with DPL. In addition, each code can be used either "normal" or "inverted." Also...it is considered to be more difficult to scan for DPL codes than TPL, although with some of the newer available receivers, this isn't necessarily still true.

We have a UHF system of approximately 150 radios, working both through a repeater and direct. We use DPL on all signals, including both the input and output of the repeater. The next time we do a big reconfiguration of our system requiring radios to be reprogrammed, we are going back to TPL. There are two reasons for this:

--DPL takes too long to decode--a significant fraction of a second. We've had difficulty training our users to wait for the path to be established before trying to talk.

--There are a large number of TPL codes. If there is not an unused code available, it's very likely that the channel is overloaded anyway.

Having said that, it is likely that there are some really good applications for DPL. We've not had to move to narrow channels yet, but I suspect that there may be good reasons to prefer DPL with the reduced bandwidth.

But...since you are coming from a carrier squelch system where your users are conditioned to be able to talk immediately when they press PTT, I'd be inclined to use TPL in your application.

Regards,
LP

Monty · Post by **Monty** » Mon Oct 28, 2002 10:05 am

Hi:

If you want some additional support, I too can
vouch for LP's views on the DPL vs PL issues.

If you live in a area where communications is
very low, then I to whould chose ( PL ) over DPL
since PL has a noticable faster response time, and
is compatable with just about every radio...

With DPL, some older Radios are not compatable
with them.....But with what you have listed, PL
will work just fine.

If you should get neighboring interference, then
just fo to DPL, and well, there are many codes
to chose from.

In addition, most chose tone freqs below 100Hz
whern using standered PL.

At these freqs or lower, in mpost radios you will
not notice the Sub-carrier Tone ( Unless the Dev
is set to high )

MS

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Mon Oct 28, 2002 10:10 am

I've heard people talk about DPL decode times. Does someone have these numbers down on paper?

It certainly can't be any worse then using a low PL tone, in decode time.

I'm not trying to be a pest. I am just courious if anyone has the numbers to back these claims up.

ExKa|iBuR · Post by **ExKa|iBuR** » Mon Oct 28, 2002 10:20 am

Heres my experiences.

Back where I used to live (Niagara Falls), I got asked to help set up a small taxi company's radios.

They were using DPL compatible radios (Maxtrac 100 mobiles)

Well, they had severe problems in the past with some moron and a ham radio playing on their frequency.

Well, I made the choice to use DPL.

I didn't know what kind of radio this other guy was using, but, figured, by going DPL, that'd be the best chance to get rid of him.

Sure enough, you'd hear him key up and stuff if you were in monitor mode, but the regular radios never heard a thing.

The guy was eventually busted for talking to the police dispatcher BTW.

Mike

larryepage · Post by **larryepage** » Mon Oct 28, 2002 12:08 pm

I have not done a rigorous measurement of decode times, but have done an "observational analysis" on several occasions. On our R1225 repeater system, using GP300, GP350, P1225, and HT750 portables, the decode time for the overall path (portable radio to repeater to portable radio) appears to be about one third of a second. With our old system (Two GM300 radios plus a RICK), the time was longer...maybe closer to half a second. This is equivalent to approximately one spoken word. Times are about the same with my Saber IIIs.

Several questions can be asked. I don't know the answers to them.

1. Is the time shorter with a "real" repeater?

2. What is the delay with TPL? It appears to be too short to estimate. Three cycles of a 100 Hz tone is less than 1/30 of a second...an order of magnitude less than the observed DPL times.

3. Does TPL decode time vary with frequency?

Again...I do not claim to be an expert in this area and would also be interested to see the claims for expected performance and even some real measured values. But I can vouch from observation that there is a noticeable difference.

Regards,
Larry Page

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Mon Oct 28, 2002 12:36 pm

Monty wrote:
In addition, most chose tone freqs below 100Hz
whern using standered PL.

At these freqs or lower, in mpost radios you will
not notice the Sub-carrier Tone ( Unless the Dev
is set to high )

Wait a second, this can't be an issue.

The audio that comes out of most radios is high-passed somewhere around 250 Hz. This can vary slightly with radio maker and model. SO... the PL/DPL doesn't make it to the speaker with the rest of the recieved audio.

Monty is correct, though, if the deviation is set way too hot, you might see harmonics going up into the received audio.

The only way that you would hear the full audio (which includes the PL/DPL) is if the radio was recieving in CSQ (monitor button,) or lacked a high-pass filter on the recieved audio.

Am I right?

As usual, please don't beat on me.

Post by **HumHead** » Mon Oct 28, 2002 2:01 pm

I'll let the radio pros finesse this, but here's some sound guy input:

1) Any audio passed through the audio amp should go through the high-pass filter, even in CSQ.

2) All audio filters have a slope. They are not hard 90 degree corners in the response curve. As a result, if you have, for example, a 24dB per octave high pass filter starting at 300Hz, the received audio will be down by 24db at 150Hz (1 Octave), 48dB at 75Hz (2 Octaves), but only 12dB at 225Hz (Half an Octave). As a result, you will hear more of the higher frequency TPL tones in the audio that passes through the high-pass filter.

Try an experiment- Get two radios, and try listening to empty carrier with a low, medium, and hign frequency TPL tone. You should be able to hear the difference in the received audio.

Now for the pros: Any idea how steep the high pass filters in most radios actually are, and where the knee point is?

Nand · Post by **Nand** » Mon Oct 28, 2002 2:37 pm

Nand · Post by **Nand** » Mon Oct 28, 2002 2:50 pm

larryepage · Post by **larryepage** » Mon Oct 28, 2002 2:54 pm

Lots of good info in this thread...

Keep in mind that the deviation of the PL tone should be probably 750 Hz or less, compared to overall peak deviation of, say 3500-4000 Hz and average deviation of maybe 1500 Hz or so. That by itself puts the PL signal maybe 3 - 6 db below the average audio before any filtering is applied. Then, in addition to the filtering of the received audio, the response of most speakers used in two-way radios (especially in portables) isn't going to reach below the 300 Hz bottom end of the communications frequency response range (nominally 300-3000 Hz). The highest frequency PL tone that I can recall without looking at the table is about 250 Hz, which is close to a third of an octave below the 300 Hz cutoff.

Putting this all together for the worst case (250 Hz)...(and using the 24 db / octave estimate provided earlier for an estimate of the filter slope), we're looking at -8 db from the filter, another -4 db or so from the lower deviation level, and maybe another -5 db from the speaker response. This all adds up to -17 db, which is a lot better than the -12 db quieting spec listed and close to the -20 db quieting spec we used to use. So even using these estimates, the likelihood of hearing the PL tone in a properly functioning radio is not very high.

Whew! I'm tired. Now if someone can come up with real slopes, I'm betting we can refine this further and that the real results will be better than this gross estimate.

Regards,
LP

RKG · Post by **RKG** » Mon Oct 28, 2002 5:17 pm

I agree this is an interesting thread.

The appendix to the most recent edition of the Quantar service manual has some curves show audio response at the AuxRX pin and at the AuxPL pin (the latter being essentially discriminator audio). This is not exactly the same as a pass curve on the high pass filter, but the overall effect is the same. Our experience has been that the higher PLs are often audible on the received audio.

There was once a pretty good piece in a GE manual on this subject. I haven't looked to see if I still have it, but I remember that the "average" time allotted for for PL validation was 155 msec; less for higher PLs and more for lower PLs. Interestingly, the alloted time for DPL detection was the same (DPL is sent at approximately 130 Hz).

I am intrigued by Nand's observation of harmonics on a DPL data stream and I can't wait to see if I can see them on a scope. From experience, DPLs are widely used in my area -- primarily because they make it harder for people to read them or bootleg them -- without apparent problem.

While higher PLs are capable of being detected and validated more quickly than lower PLs (since the zero-voltage crossings come faster), many systems use a fixed time for PL/DPL sampling, so the advantage of a higher PL as a means of lowering composite attack time may be more theoretical than real.

Nand · Post by **Nand** » Mon Oct 28, 2002 8:04 pm

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Mon Oct 28, 2002 8:44 pm

In regards to the "splatter" of the DPL code into the audiable audio:

Here are what some service schematics for Motorola DPL boards say. These are all taken from Motorola document 68P81106E83-A, "Digital Private Line Binary-Coded Squelch Theory and Servicing Fundamentals." These cover DPL boards for Micor Bases, Repeaters, Mobiles. Also, Mocom70 Mobiles and Consolette. These were the first Motorola radios to use DPL.

Please be advised that this could get boring, if you aren't much of a geek.

TTN6003A DPL Simplex encoder schematic, the DPL signal goes through a 140 Hz low-pass filter. It says above it "8 db per octave attenuation above 140 Hz."

TLN5725A DPL Duplex encoder schematic, the DPL signal goes through a 140 Hz low-pass filter. It says above it "18 db per octave attenuation above 140 Hz."

I should note that the low-pass filter electronics for these two boards looks almost identical, and most of the electronic part values are the same. Perhaps either 18 db or 8 db is a typo?

The TLN5725A "Duplex DPL Encoder," TLN5723A, TLN5724A, & TLN5726A "Simplex DPL Encoder," and TLN5817A & TLN5817AV "DPL Squelch Encoder-Decoder" all say the same thing... "Q821 is on during PTT. When on, Q821 switches Q803 into the active filter to shift the -3db point of the filter response down to about 85 Hz. When Q821 turns off, the -3 db point of the filter response shifts up to about 140 Hz. This allows proper transmittion of the turn-off code during 180 mS following unkeying." I should mention that the Q numbers of the transistors vary model to model.

Will · Post by **Will** » Tue Oct 29, 2002 1:33 am

At the first part of decoding or "validating" a DPL code the decoder is looking at fewer bits in the complete word, but it requires almost two complete words to detect the code and then the decoder goes into a more strict decoding looking at ALL bits of the word to fully decode. This (Motorola) was to be able to overcome the extra time it took to decode a DPL word, but not falsley decode a simmular word. As Nand stated, in the REAL world of repeaters anywhere from 500 to 1400ms for a DPL signal to get from the transmitter thru the repeater and decode the mobile/portable and open the speaker. PL is typically no more than 450ms, fewer cycles at a faster rate to decode. Increasing the DPL or PL deviation does not help reduce the decode times, we try to set the PL to no more than 700hz dev on a 5khz system. Any more than 500khz PL dev is not any better and just reduces the space for the voice dev.
AVOID using 118.8, 67, and 123 hz PL tones due to broken repeaters with bad power supplies generating intermod and being decoded in your repeater receiver. The second harmonic of 60hz, and most power supplies are full wave and have 120hz ripple, capacitors get weak and the intermod and other interferance gets out of hand. Sometimes even a PL code of 179.9hz, 3X 60hz, gets hit.

And YES the R1225 has a much better /faster decoder/encoder than the seperate GR series with two GM radios. Then add the GM radio's decode delay and transmitter key-up+encode time + RICK time in the and the "decode' time IS longer.

RKG · Post by **RKG** » Tue Oct 29, 2002 9:46 am

Now you all have me curious, and I'm going to spend a whole day figuring out how to set up a dual input scope to measure the time between key down on an input signal and when the DPL decoder signals valid. I accept the math, but from experience watching the LEDs I can't believe it is as long as a full second.

Does anyone know of M recommends a longer PDC pre-time if DPL is being used versus PL? Around here 400 msec is common without regard to tone.

Nand · Post by **Nand** » Tue Oct 29, 2002 3:21 pm

Post by **xmo** » Tue Oct 29, 2002 5:44 pm

The way we used to teach it in DPL school was 23 bits @ 7.44 ms. = 171.12 ms. word length.

A very complete description of the operation of DPL was published in the April 1979 issue of Communications magazine. This article claims the DPL decode time is less than 200 ms.

The article explains how the bits are sampled several times per bit and the samples loaded into a long shift register which is then compared at high speed to the stored (desired) code.(rolling code so only one word time is required to decode)

NAND's idea of running tests is interesting. One possible way would be to generate a signal containing the proper code with a service monitor. Connect that to the target radio through an antenna relay. Apply voltage to the relay and use the same signal to trigger the scope. The relay should apply RF to the receiver much faster than a transmitter (which could have its own turn on time which is certainly a concern in terms of the total system audio path turn on time but should be understood independently from the actual DPL decode time)

The main trace signal applied to the scope input would be the audio unmute line. Performing this test several times and averaging the results should answer the question of whether one code word time, one and a half, or two are required.

Nand · Post by **Nand** » Tue Oct 29, 2002 6:04 pm

Post by **xmo** » Tue Oct 29, 2002 6:20 pm

Ooops....

RKG · Post by **RKG** » Tue Oct 29, 2002 6:32 pm

Thanks, pal; I was nearly to the end of this thread thinking that someone else had become sufficiently intellectually ensnared as to spend the whole day chasing this issue.

Seriously, Nand's and xmo's numbers seem to jibe more with experiential observations. And if I'm right that 400 msec is a common (and workable) setting for MDC pre-time (in the mobile radio), and that an MDC decoder does not start to decode until the repeater or comparator has completed its composite attack sequence (COR valid, DPL valid, squelch gate enable), with some margin to spare, don't we know that the composite attack time has to be on the order of about 300 msec?

I'm beginning to feel more secure in the conclusion that there is no meaningful distinction in attack times between PLs and DPLs.

By the way, Nand keeps reiterating the point that, for mobile-to-mobile comms, the composite attack time has to be doubled because the receiving mobile has to go through essentially the same sequence as the repeater. The point is valid and I'll acknowledge it.

xmo: any chance you could scan that article and post it somehow?

Nand · Post by **Nand** » Tue Oct 29, 2002 7:23 pm

thgiz · Post by **thgiz** » Tue Oct 29, 2002 7:47 pm

I guess i got my answer

thanks guys...

RStolting · Post by **RStolting** » Tue Oct 29, 2002 8:38 pm

I noticed this wasn't mentioned here, but Iv'e had this happen to me (actually did it to myself

) 'specially with the Visars ( what a piece of crap) anyway, they will not do all of the available DPL codes that all the other manufacturers radios can do. If you stay with /\/\ and start with a developmentally challenged radio (again Visar) and choose the codes from the MSS, ANY radio ..Kenwood, Vertex etc can do the codes.. but not always the reverse. Some purests feel any Non-/\/\ code is sacreligious, but the more codes the merrier!! Just my $.02 worth.

Nand · Post by **Nand** » Tue Oct 29, 2002 8:49 pm

Post by **xmo** » Tue Oct 29, 2002 9:30 pm

"Some purests feel any Non-/\/\ code is sacreligious, but the more codes the merrier!! Just my $.02 worth."
---------------------------------------------------------------------------------------------------------------------------

Here is what Motorola has to say on the subject of acceptable DPL codes:

"Due to inferior noise, voice, and adjacent code falsing - all 16-transition codes will be reserved for special use only.

The 35 non-symetrical codes that were found to be acceptable with respect to sensitivity and attack time were found to have a serious noise falsing problem...none of these 35 codes will be used."

Regarding decode time - a Maxtrac set up on the bench as described in previous post had the following unmute times for DPL code 114: 215, 170, 165, 195, 240, 190, 200, 165, 180, 175. Average for the ten samples 190 ms.

I guess they knew what they were talking about when they said less than 200 ms.

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Tue Oct 29, 2002 11:12 pm

RKG wrote: By the way, Nand keeps reiterating the point that, for mobile-to-mobile comms, the composite attack time has to be doubled because the receiving mobile has to go through essentially the same sequence as the repeater. The point is valid and I'll acknowledge it.

If the repeater was running in CSQ mode, this wouldn't be much of an issue, right?

Is DPL okay for simplex mobile to mobile usage?

Nand · Post by **Nand** » Wed Oct 30, 2002 4:17 am

RKG · Post by **RKG** » Wed Oct 30, 2002 7:05 am

Thanks xmo; now I don't have to wait for the next blizzard in Boston to find out the answer.

What a great thread this has been. Thanks to all.

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Wed Oct 30, 2002 10:50 am

Just FYI, beware using a PL tone of 131.8 Hz or 136.5 Hz on the same community channel that uses DPL. The DPL turn off code is 134 Hz, which might cause falsings on the PL's.

Post by **xmo** » Wed Oct 30, 2002 11:34 am

OK - OK - OK Once I get started on one of these things......

So how about CSQ & PL?

Same radio (Maxtrac) & same setup:

CSQ: 25, 32, 20, 24, 32, 16, 18, 24, 14, 30. Average 23.5 ms.

PL 67.0: 206, 201, 160, 218, 186, 226, 204, 205, 146, 154. Average 191 ms.

PL 250.3: 232, 234, 230, 189, 232, 219, 205, 245, 181, 217. Average 219 ms.

67.0 and 250.3 are the lowest and highest codes the Maxtrac will do. I kind of expected the higher freq. PL to be faster but maybe it is too close to the filter cut-off. A mid range tone in the 150 to 190 Hz range might be faster - may try that later.

RKG · Post by **RKG** » Wed Oct 30, 2002 12:29 pm

Some thoughts:

1. Thanks xmo. Now I can enjoy the next blizzard.

2. I'd be inclined to attribute the spread of the individual readings to jitter in the test setup. The averages are what counts.

3. I'd be inclined to view all three sets of data (DPL, low PL and high PL) as the same.

4. Which makes me wonder: what if the controller logic sets a fixed window for decoding of tone/DPL, regardless of format or value? Then it really wouldn't make any difference.

5. I'll bet the price of donuts that this same question will come up a year from now. Hope someone then will be able to locate this thread when it happens.

Post by **xmo** » Wed Oct 30, 2002 1:37 pm

"I'd be inclined to attribute the spread of the individual readings to jitter in the test setup..."
-----------------------------------------------------------------------------------------------------

Now that is an evil thing to do - sowing the seeds of doubt!

My thought process was that the scope is triggered by the application of DC to a brand new antenna relay which should close (and apply RF to the radio) in microseconds - many orders of magnitude faster than the radio decode time, thereby becoming inconsequential to the measured results.

One possible way of verification would be to split the RF from the antenna relay to two identical radios programmed the same. If there are variations from test to test but not between radios - then the "jitter" is in the set-up. If, on the other hand, the radios decode with random variations between each other - it is a radio issue.

larryepage · Post by **larryepage** » Wed Oct 30, 2002 2:03 pm

I did a little statistical analysis of the data supplied by XMO. (There wasn't particularly a reason to do so, but that's just what I do in my real job, so...) The results are statistically valid, but you may choose to consider that they are or are not important. It's up to you, so you can either read on or stop here...

The results were interesting for a couple of reasons. First, there is a statistically significant difference between the average of 218.4 ms for TPL=250.3 and the 190.6 ms for TPL=67, and between TPL=250.3 and DPL=114 (189.5 ms). TPL=67 and DPL=114 are statistically equivalent. This is very different from what my observational experience had told me, and it points out the validity of doing an experiment and collecting measured data.

What is also interesting is that the standard deviation for CSQ is about 6 ms. In other words, it is very consistent. For all three of the coded squelch experiments, the standard deviation was about 25 ms, 4 times as great. (Actually, it ranged from 21 ms to about 28 ms). This means that the expected spread of unsquelch times over a large number of transmissions is about 150 ms...almost equal to the average time. So statistically, we would expect that the worst unsquelch time would be almost twice as long as the best case.

In other words, given this data, it is likely that for any single observation, the time we see would be expected to vary pretty widely... There is yet an unanswered question, however, in how much difference we see between different radio models. Specifically, Spectras are known for turning around very quickly between transmit and receive, and it seems there have been comments on this board that MCX1000s are very fast also.

Anyway...thanks for this thread. It has been interesting and useful, and has helped dispel some misconceptions that I have had.

Regards,
LP

Nand · Post by **Nand** » Wed Oct 30, 2002 4:45 pm

Post by **xmo** » Wed Oct 30, 2002 6:28 pm

More data:

Added a splitter and a second identical Maxtrac (Radio #2 in the results) Each measurement (a single trigger event) produced two results - a time for radio #1 and a time for radio #2.

Test #1 PL 141.3

Radio#1: 230, 216, 179, 212, 205, 135, 179, 172, 208, 121. Average 186 ms.
Radio#2: 152, 161, 200, 190, 206, 114, 249, 218, 190, 215. Average 190 ms.

Test #2 DPL 114

Radio #1: 290, 209, 171, 160, 139, 187, 207, 141, 192, 171. Average 187 ms.
Radio #2: 225, 144, 174, 275, 188, 192, 213, 191, 201, 176. Average 198 ms.

Another test: Micor satellite receiver C03RTB with a TRN6083 PL decoder and a 3A reed (127.3 Hz)

Test #3: 214, 228, 212, 213, 215, 217, 216, 227, 221, 214. Averave 218 ms.

Conclusions:

1. The variations between radios in tests #1 and #2 and the consistency of results in test #3 suggest there is negligble jitter in the test setup.

2. A reed type decoder is more consistent than a Maxtrac.

3. There is no significant difference in decode time between PL and DPL.

4. An accurate generalization would be to say that coded squelch takes about 1/4 second to decode whereas CSQ is less than 1/10 second.

Now - to address the question: How can the Maxtrac decode DPL in less than one word?

The shift register used to hold the code starts out filled with random 1s&0s derived from the noise present before the signal arrives. As the real bits are filling the register, the MPU is attempting to get a pattern match within an allowable range of errored bits. Assuming the signal is clean, good data will displace the random data and at some point before an entire word is received the error threshold will be passed and audio will be enabled.

RKG · Post by **RKG** » Wed Oct 30, 2002 6:51 pm

xmo: take down the test set-up or you'll be up all night.

Nand: is the mobile exciter likely to survive continuous duty?

The reed decoder data is eye-catching: not only does it dispell the assumption that there is inherent variability in the test setup, but it also tends to prove that reeds are more consistent than digital decoders. I would have suspected the reverse.

Nice job, guys.

Nand · Post by **Nand** » Wed Oct 30, 2002 7:40 pm

Nand · Post by **Nand** » Wed Oct 30, 2002 7:49 pm

Post by **xmo** » Wed Oct 30, 2002 8:47 pm

Nand - I agree with your idea that some of the random bits would match real bits - if this weren't possible falsing could never occur & we know that it happens. Probably the shortest decode times are a combination of real bits and code-correct noise bits that collectively pass the error threshold.

The masked board being different is also possible as is the thought that the firmware in other products (newer products?) may have more consistent decode times.

I think I have had enough fun with this one for now but maybe it will snow in Boston and curiosity will get the best of RKG. It would be interesting to see test results for some other products like XTS3000, Spectra, and Pro-series!

RKG · Post by **RKG** » Thu Oct 31, 2002 1:47 pm

Post-script: "DCS employs a fixed octal digit 4 as the first digit, followed by three octal digits [from the code table]. Code words are 23 bit-long strings: 12 bits of octal code followed by 11 bits of CRC [error checking]. Each bit is 7.5 ms, adding up to 172.5 ms per word. While it might appear that 512 codes are possible, only 83 exist, because a code word that is misaligned when serially shifted into the decoder can match a different code word." Believe this comes from the EIA document on DPLs (found it in some old notes).

Glen W Christen · Post by **Glen W Christen** » Thu Oct 31, 2002 2:46 pm

I agree with NOT using 136.5 as a TPL. The turn-off code from DPL on the same frequency WILL cause every receiver on that code to false everytime someone unkeys on any DPL. When M was still in the conventional community repeater business, I had to change codes for the poor soul usiing 136.5 before they went insane.

Nand · Post by **Nand** » Thu Oct 31, 2002 7:47 pm

RKG · Post by **RKG** » Thu Oct 31, 2002 8:06 pm

And note what Com-Spec says about decode time (171 ms).

The bad news is that we seem to have reinvented the wheel.

The good news is that, like the first guy, we got it round.

Jonathan KC8RYW · Post by **Jonathan KC8RYW** » Sat Nov 02, 2002 5:52 pm

There is an easy to read explaination of DCS at:
http://mmi-comm.tripod.com/dcs.html

TPL versus DPL

TPL versus DPL

TPL vs. DPL

Decode Times for DPL

DPL Codes

Re: DPL Codes

Statistical Analysis

DPL vs PL