Dr. Riki Morikawa, George Mason University
 

PCM and T-1 Framing

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Channelized T-1 Frame

We know that T-carriers are guided dedicated digital lines that are provided on a leased-service basis.  As a digital carrier, the data needs to be formatted in such a manner so that it becomes meaningful to the communicating ends (vice just a stream of 1’s and 0’s with no start/stop or control, etc.).

The T-1 frame is the most basic (note, slightly different from E-1 frames that you will find overseas).  The T-1 supports a data rate of 1.544 Mbps, and incorporates PCM, which enables us to code analog voice into a voice-grade digital one. So let’s start with PCM:

We know that typical voice occupies a range from 100Hz to 8000Hz; however for telephone voice-grade (i.e., what is needed to identify an individual’s voice) we only need to capture 300Hz to 3400Hz.  Therefore, the frequency bandwidth is 3400 - 300 = 3100 Hz, however, using PCM, we round up to 4kHz.

We now want to sample analog voice with a frequency BW of 4kHz, however, Nyquist tells us that we must sample the analog stream at approximately double the frequency BW in order to avoid “aliasing” the signal which results in distortion at the other end.  So our Nyquist sampling rate is fs ≥ 2 x BW_freq or  8000 samples per second.

Next, we need to assign a bit sequence to represent the analog amplitude (e.g., voltage) of our signal per sample.  In the case of PCM, 8 bits are allocated to each sample.  That means that the number of voltage levels that we can represent digitally is 2⁸=256 unique voltage levels.  The process of assigning a digital sequence to a sampled amplitude is called encoding.  (Note:  the formula 2^N=M (voltage levels), where N equals the number of bits)

Since you have to push 8 bits of voice data every second for a sampling frequency of 8ksps, we find that we have a data rate of:  8bits/sample x 8000samples/sec = 64kbps to represent one uncompressed voice grade channel.

Now let’s get back to T-1:

A T-1 frame supports 24 voice grade channels (note: not 24 64kbps channels in a single frame, but one byte of each 24 DS-0 channel per T-1 frame).  Each voice grade channel (DS-0) is, not surprisingly, 64kbps.  So one T-1 frame:

                T-1 Frame supports one byte of a single DS-0  voice channel for a total of 24 bytes from 24 separate DS-0 voice channels, plus one framing bit

                T-1 = [8bits * 24 DS-0s] + 1 framing bit = 193 bits per frame

Since 24 DS-0 channels do not fit into a single T-1 frame, and because we must meet the criteria of pushing 64kbps for voice grade channels, we must push many T-1 frames in a single second.

Let’s take the case of a single DS-0 byte within a T-1 frame.  In order to meet the 64kbps requirement, we need:

                8 bits per frame * 8000 T-1 frames per sec = 64kbps

So for a T-1 line, we experience 8000 T-1 frames per second supporting 24 DS-0 voice grade PCM channels.  i.e., We must push 8000 T-1 frames/second.