Quantum Communications - Part 3: Photon Polarization and Superposition

 Building on Part 2’s discussion of polarization, let's look a little deeper at how light enables quantum communication. Superposition in quantum mechanics means a photon can exist in multiple polarization states at once, unlike classical objects that must be in one definite state. Looking at the diagram below, a photon isn't limited to being just vertical (1) or horizontal (0), but can exist in a mixture of both until measured. Think of it like a spinning coin - while spinning, it's neither heads nor tails but both possibilities at once. When we measure the photon's polarization (like catching the coin), it "collapses" into one definite state.

The diagram shows two measurement bases - rectilinear and diagonal. A photon in superposition measured in either base has a probability of being found in either state of that base. This property is crucial for quantum cryptography because any measurement by an eavesdropper forces the superposition to collapse, altering the photon's state and revealing the intrusion.

 

The 45° polarization state, shown in the diagonal base of our diagram, demonstrates one of the most fascinating aspects of quantum mechanics. While we might classically think of 45° as simply an angle halfway between horizontal and vertical, in quantum mechanics it represents something far more profound. When a photon is polarized at 45°, it literally exists in a perfect blend of horizontal and vertical states at the same time - not just leaning one way or the other, but fully in both states simultaneously.

 

This quantum behavior becomes clear when we measure these 45° polarized photons. If we measure using the rectilinear base (horizontal/vertical as shown in the left circle of our diagram), we get the following result: the photon will randomly show up as either horizontal or vertical with exactly equal probability. This isn't because we're measuring imprecisely or because the photon was "kind of" in both states - it was genuinely, mathematically, and physically in both states at once until the act of measurement forced it to pick one.

 

Think of it this way: if we send many 45° polarized photons through a horizontal polarizer, exactly half will pass through (registering as horizontal) and half will be blocked (registering as vertical). This isn't due to some classical "angled" behavior - it's a direct manifestation of quantum superposition, where the photon existed in both states simultaneously until we forced it to "decide" by measuring it.

 

This property is part of what makes quantum communication so secure: any attempt to measure these superposition states unavoidably disturbs them, making eavesdropping detectable.

Quantum Communications - Part 2: Polarization

In Part 1 of this series I discussed how quantum superposition allows particles to exist in multiple states at once until measured. This makes quantum information almost impossible to copy secretly, enabling ultra-secure communication systems that can detect eavesdropping attempts. Here we'll take a closer look at how this information is transmitted using light particles called photons. 

Light can be analyzed as either a ray or a wave, each model revealing different aspects of its behavior. The ray model treats light as straight lines traveling through space, useful for understanding reflection, refraction, and how lenses and mirrors work. The wave model shows light as oscillating electromagnetic waves, explaining phenomena like interference, diffraction, and polarization. While the ray model helps us design simple optical devices like eyeglasses, the wave model is necessary for understanding more complex effects like how polarizing filters work. Both models remain important in modern optics, with each being used depending on which aspects of light's behavior are most relevant to the situation at hand.

 

When it comes to polarization we need to think about light as a wave. Light waves oscillate perpendicular to their direction of travel, Unpolarized light ( like we get from natural sources like the sun or artificial sources like light bulbs) vibrates in all possible directions like a rope being waved up-down, side-to-side, and at every angle in between. A polarization filter works like a microscopic venetian blind with extremely fine parallel slits. When light encounters the filter, only the waves that vibrate parallel to these slits can pass through completely. Waves vibrating in other directions are either blocked entirely or have only their parallel components transmitted. The light that emerges from the filter is polarized, meaning all the waves are vibrating in the same direction. 

Here's a quick 3 second video I made demonstrating light passing through a polarizing filter.

Before the filter: 

• Horizontal component (blue wave)
• Vertical component (pink wave)
• 45-degree component (green wave, thicker line) All components are present in the unpolarized light

The Filter: 

• Oriented at 45 degrees
• Only allows waves aligned with its transmission axis

After the filter: 

• Only the 45-degree component (green wave) passes through
• Horizontal and vertical components are blocked
• The transmitted light is polarized along the 45-degree axis

Notice:

• Only transmits light waves that oscillate parallel to its transmission axis (45 degrees in this case)
• Waves at other angles are either blocked or have only their 45-degree component transmitted
• The result is polarized light oscillating only at 45 degrees

This selective transmission property makes polarizing filters particularly useful in everyday applications. For example, polarizing sunglasses can effectively reduce glare because light reflecting off horizontal surfaces like water or roads tends to become partially polarized in the horizontal direction. The sunglasses, which have vertical polarizing slits, block this horizontal glare while still allowing other light through. A demonstration of how polarization works involves using two polarizing filters. When light passes through the first filter, it becomes polarized in one direction. If you then rotate a second filter 90 degrees relative to the first, no light gets through at all because the polarized light from the first filter is now perpendicular to the slits in the second filter.

 

So what does polarization have to do with quantum communications? In quantum communications individual photons can be prepared in specific polarization states (vertical, horizontal, or diagonal) to represent quantum bits. Due to quantum mechanics principles, any attempt to measure these polarization states disturbs them, making secure communication possible - eavesdropping can be detected. Polarization also enables quantum entanglement, where measuring one photon's polarization instantly determines its entangled partner's state, even at a distance.

 

While powerful, polarization methods face practical challenges as polarization states can degrade during transmission through optical fibers or atmosphere, requiring sophisticated error correction methods. For these reasons, quantum communications can use several alternatives to polarization for encoding quantum information. Time-bin encoding uses photon arrival times and works well in fiber optics where polarization degrades. Phase encoding utilizes phase differences between photon paths, while frequency encoding uses different photon frequencies. Orbital Angular Momentum (OAM) encoding exploits spiral patterns of light waves, potentially carrying more information than polarization. Path encoding, which uses different physical routes for photons, is useful in integrated photonic circuits. Each of these methods has its own advantages and the choice often depends on the specific application and transmission medium being used. For instance, time-bin encoding tends to be more robust for long-distance fiber communication, while OAM can potentially carry more information per photon. 

Quantum Communications – Part 1

 Computers, communications, photonics, cybersecurity…… some of my favorite technologies all bundled together in quantum communications! But… what is it? How does it work? Let's take an introductory look.

In quantum mechanics, something called superposition allows systems to exist in multiple states simultaneously - like a spinning coin being both heads and tails at once, until observed. Only measurement forces it into a definite state. This principle affects quantum information through the no-cloning theorem, which states that it's impossible to create an exact copy of an unknown quantum state due to quantum mechanics' mathematical foundations. This feature enables quantum key distribution (QKD), which creates unbreakable encryption keys. Any eavesdropping attempt disturbs the quantum states due to the no-cloning theorem, instantly revealing the intrusion. While classical information can be copied perfectly, quantum information's resistance to copying both protects it and makes quantum teleportation the only way to transfer quantum states.

 

How about an example? Let’s now compare sending a classical letter and sending a quantum letter using two diagrams I’ve created. These diagrams split into two parallel workflows showing classical versus quantum communication highlight the key security advantages of quantum communication over classical methods.

 

The classical letter path shows a letter that can be intercepted, read, and copied without detection as it moves from sender to recipient through the postal system.

The quantum letter path illustrates how quantum letters behave differently:

• The letter exists in superposition (blue state) until measured
• Any attempt to read/copy disturbs the quantum state (changes to red)
• This disturbance is detectable when received by the recipient, revealing tampering

We’ll dig a little deeper in future posts – for now think of quantum communication as the first step toward a quantum internet - one that operates on the powerful principles of quantum physics rather than classical physics. While we may not see quantum email on our phones anytime soon, the technology is steadily advancing from science fiction toward practical reality.

Closing the loop with IP/Optical Integration

I've spent the last 17 years focused on Internet Protocol (IP) over various transport systems - wired (copper), wireless and optical. With the explosion of video, social media and other bandwidth hungry applications we've seen fiber moving closer and closer to the end user. Wireless is the perfect example with towers back-hauled into the network by fiber. It's really just the last mile/final connection that is typically not optical fiber based for most of us.

We're seeing IP/optical integration today really ramping with these things called software defined networks (SDNs). I wrote a post defining and describing SDN's last month titled SDN: When The Hardware Becomes A Little More Soft

With the move to all-IP, SDN and cloud services, many service providers are now integrating IP routing and transport. In this short 4 minute and 50 audio clip, Arnold Jansen discusses how IP/optical control integration can help operators simplify and streamline their operations and drive better cost synergies.



 Smart, fast, efficient. Good stuff.

Verizon Trimming Some Wireline Limbs

I've been teaching Verizon technicians in a program called NextStep since the mid 1990's. The Next Step Program allows contract qualified Verizon associates who are members of the Communications Workers of America (CWA) or the International Brotherhood of Electrical Workers (IBEW) to earn an Associate in Applied Science degree in Telecommunications Technology from a participating college. It's been a great opportunity for everyone involved to keep up and learn as the industry has transitioned.

This morning I taught my first class of the fall semester and we had some interesting discussion on where copper based landline services like DSL are going. The other night on Jim Cramer's show, Verizon CEO Lowell McAdam opened up a bit on the companies plans. Here's some back and forth from the show posted at  Stop the Cap!:

Jm Cramer, CNBC: “[Under former Verizon CEO Ivan Seidenberg, Verizon] took areas that really weren’t growth areas and sold them to Frontier and other players. Would you be able to get rid of some of your underperforming landline businesses to be able to increase [Verizon's] growth even further?”

Lowell McAdam, Verizon: “That is a possibility. [...] If you talk about opportunities here, now that we have One Verizon, [...] we are going to trim some limbs around the tree here. Things that aren’t performing will not be a part of our portfolio so we can invest in things that will drive the kind of growth we are excited to be able to tap here.”

In New Jersey and New York, Verizon is moving on a wireless landline replacement called Voice Link. It's optional for some customers but many are thinking it will replace copper services in there is approval from the states regulators. Verizon is calling Voice Link an improvement for voice customers dealing with repeated service calls.

Bloomberg estimates the Verizon wireless net worth is around $289 billion while Verizon wireline (landlines, FiOS and business broadband) is worth just $24 billion. Looking at revenue, Bloomberg says Verizon wireline totaled $39.8 billion last year which is down from $50.3 billion in 2007. During the same period, Verizon wireless revenue was up 73% to $75.9 billion.

It's pretty clear where this is all going - at least when it comes to Verizon wireline.

You can read a transcript of the complete McAdam interview linked here.

Watching What You Do While You Watch TV

Verizon recently filed a patent application that would target television ads using real time information collected by infrared cameras and microphones in you DVR. This is wild stuff - here's some examples of how this system would work right out of the filed document:

• if detection facility 104 determines that a user is exercising (e.g., running on a treadmill, doing aerobics, lifting weights, etc.), advertising facility 106 may select an advertisement associated with exercise in general, a specific exercise being performed by the user, and/or any other advertisement (e.g., an advertisement for health food) that may be intended for people who exercise. 

• if detection facility 104 detects that a user is playing with a dog, advertising facility 106 may select an advertisement associated with dogs (e.g., a dog food commercial, a flea treatment commercial, etc.). 

• if detection facility 104 detects one or more words spoken by a user (e.g., while talking to another user within the same room or on the telephone), advertising facility 106 may utilize the one or more words spoken by the user to search for and/or select an advertisement associated with the one or more words. 

• if detection facility 104 detects that a couple is arguing/fighting with each other, advertising facility 106 may select an advertisement associated marriage/relationship counseling. 

• if detection facility 104 detects a particular object (e.g., a Budweiser can) within a user's surroundings, advertising facility 106 may select an advertisement associated with the detected object (e.g., a Budweiser commercial). 

•  if detection facility 104 detects a mood of a user (e.g., that the user is stressed), advertising facility 106 may select an advertisement associated with the detected mood (e.g., a commercial for a stress-relief product such as aromatherapy candles, a vacation resort, etc.).

The image posted is also from the patent application and shows the detection zone. 

Pets, people, conversations, moods, beer cans?? I don't think this is something I'd want in my home.

Data Transmission on T1 Carriers - Part 2

In Part 1of this topic I described how a T1 carrier is used to transmit data. Data transmission by nature is "bursty" meaning large amounts of information are typically transmitted and then followed by relatively quiet transmission periods. This can cause transmission problems for T-carrier systems since they rely on timing synchronization. Let's take a look how this potential problem is avoided.

Data Transmission on T-1 Carriers Part 1

Back in December I wrote a post here titled T1 Lines - What They Are. In the post I discuss the Digital Signal (DS) Level System and how combining the equivalent of 24 DS-0 voice channels along with overhead consisting of timing and synchronization bits brings the DS-1 bit rate to 1.644 Mbps - that's a T1. In this post, let's have a look in more detail to get a better idea of how the entire system works. 

The T-1 Carrier uses time division multiplexing and was designed for voice call transmission. When used for data one would think it would be possible to achieve a data bit rate of 64 Kbps over a T-1 carrier. Looking a little closer one sees that data on T-1 carriers is transmitted in the form of only 7 bit words, all eight bits are not used. Why? 

Remember the T carrier system was initially designed for voice. The first signal synchronization used for the T-1 carrier substituted a single in band signaling bit, used for control, for each of the 24 channels in every sixth frame. This means in the sixth and twelfth frames of every T-1 carrier master frame there is a bit used for in-band signaling. This is referred to as bit-robbing. Bit robbing is usually not a problem when transmitting voice. Even though the signal is slightly distorted, the listener on the receiving end cannot perceive the distortion. However this is a major problem when transmitting data as any data received with missing bits will be distorted and received incorrectly. To eliminate the problem caused by bit robbing data on the T-1 carrier is limited to seven bits per frame in all frames. By decreasing the number of bits transmitted the data bit rate is reduced.

For this reason, 56 Kbps Clear Channel Capability is the term used to refer to the T-1 carrier single channel maximum data bit rate.

T-1 Carrier Pulse Cycles

If we look closer at a T-1 Carrier signal we see there are negative and positive pulses combined in the digital pulse train. A sample T-1 signal pulse train is shown in the figure below.

Sample T-1 Pulse Train

It has been found that alternating positive/negative pulse trains (bipolar) produces fewer transmission errors than all positive or all negative pulse trains. These pulses are used to represent binary 1’s and each pulse, when non-zero, is positive half the non-zero cycle (50%) and negative half the non-zero cycle. We can look at an example of a positive (cycle 1) and negative (cycle 4) pulse from the above figure.

Sample T-1 Positive and Negative Going Pulses

In the figure above, T represents the period, or time it takes to complete a single pulse cycle. We can calculate the percent duty cycle using the following equation:

The pulses here are not zero for one half of the pulse period and have a 50% duty cycle. Let’s go back now and look at the original pulse train diagram and look at each cycle:

You can now see that if a pulse is present within a cycle time slot, whether positive or negative, it represents a 1 bit and if no pulse is present, it represents a 0-bit.

In Part 2 of this series I'll cover something called Bipolar with Zero Substitution (B8ZS) for T-1 signal synchronization.

Is You Legal Right To A Landline Phone Going Away?

You may not realize it but you have a legal right to have landline phone service at almost any address in the United States. The Goals of Universal Service, as outlined in the FCC Telecommunications Act of 1996 are to:

• Promote the availability of quality services at just, reasonable and affordable rates for all consumers
• Increase nationwide access to advanced telecommunications services
• Advance the availability of such services to all consumers, including those in low income, rural, insular, and high cost areas at rates that are reasonably comparable to those charged in urban areas
• Increase access to telecommunications and advanced services in schools, libraries and rural health care facilities
• Provide equitable and non-discriminatory contributions from all providers of telecommunications services to the fund supporting universal service programs

Universal Service goes way back to 1913 when AT&T President Thomas Vail promised "one system, one policy, universal service" in return for maintaining AT&T's (at the time) monopoly. Times have changed and today, AT&T along with Verizon are saying universal landline service is costly and unfair due to a now competitive market for voice services.

Both companies have proposed a new set of rules that would allow them to only service the customers they want to service. Some say (including David Cay Johnston in a recent piece at Reuters) this roughly translates to the higher population and wealthy areas where people can afford bundled voice, video and data packages.

Johnston's piece says:

 State capitals are seeing intense lobbying to end universal service obligations but with little public awareness due to the dwindling ranks () of statehouse () reporters. 

The Utility Rate Network, a consumer advocate group, identified 120 AT&T lobbyists in Sacramento, one per California lawmaker. Mary Pat Regan, president of AT&T Kentucky, told me she has 36 lobbyists in that state working on the company's bill to end universal landline service.

Florida, North Carolina, Texas and Wisconsin have all repealed Universal Service but there have not been any cutbacks.... yet. 

Cell phones, cable and satellite are being proposed as options at least in the rural areas but there are limitations with each. Cell phones are expensive but there are packages for low income people starting at $2 per month. Internet calling is another option but expensive because it requires a broadband connection and a service. Satellite is another option but it's expensive and sometimes there are weather related connection issues.

Johnston finishes his Reuters piece saying:

We.... should not lose sight of the benefits of guaranteed access to affordable basic telephone service. The law should not force people to buy costly services they do not need.Nor should we forget that customers paid for the landline telephone system, including many billions of dollars in rate increases over the past two decades that helped AT&T and Verizon develop their cellular systems. 

If we lose universal service, I doubt we will ever get it back. Let's get a balanced policy rather than quietly rewriting laws to benefit one industry.

SONET Packet-Oriented Data Framing

In my last legacy PSTN post I discussed how Synchronous Optical Network (SONET) is used to multiplex, transmit and then de-multiplex voice calls. Today, let’s take a look at how SONET  is being used to transmit packet-oriented data (in today’s world - basically Ethernet).

In that last SONET post we said the SONET international equivalent is called Synchronous Digital Hierarchy (SDH). Now, when we talk about data at the SONET/SDH level we’re talking frames (think layer 2 OSI model) and the base unit of framing for SDH is something called a Synchronous Transport Module, level 1 (STM-1) with operates at 155.52 Mbps. 

In the post I also said the base SONET standard bit rate is 51.84 Mbps and is referred to as Optical Carrier  (OC) -1 or Synchronous Transport Level  (STS) -1. Now, because we’re talking 3 times an STS-1 and it is concatenated (combined), the base SONET data framing unit (running at 155.52 Mbps)  is referred to as a STS-3c (Synchronous Transport Signal 3, concatenated) which is also referred to as an OC-3c (Optical Carrier - 3c). 

Now that I have you completely confused (!) lets’s talk a little more about packet frames. A typical packet frame consists of a header, payload (the actual data being sent) and some kind of trailer. I like to use a letter analogy to understand what is going on - someone writes a letter (think of the letter as the payload or data). It gets put on an envelope (think of the envelop as the header and trailer for now). At the sending end the letter gets a destination address, a return address, etc and gets delivered. At the receiving end the letter gets opened, the envelop discarded and the letter itself saved and used.

For an STS-3c framing unit, the payload rate is 149.76 Mbit/s and overhead is 5.76 Mbit/s.

If we look at an individual SONET STS-3c frame - it’s  2,430 octets long. SONET systems transmit nine octets of overhead and then 261 octets of payload in sequence. This transmission is  repeated nine times in 125 micro-seconds until 2,430 octets have been transmitted. 

Timing is critical here (that's why it's called synchronous) for communications across the entire network.

Synchronous Optical Network - SONET

Here's another entry for what I've been calling the legacy Public Switched Telephone Network (PSTN) series. In my last legacy post we covered the European or “E” carrier system. Today, let's look at SONET.

In the United States T-1 carriers have been replaced in many locations with Synchronous Optical Network (SONET) systems. Internationally, the SONET equivalent is called Synchronous Digital Hierarchy (SDH). Both SONET and SDH systems consist of rings of fiber capable of carrying very high bit rates over long distances. Copper has been replaced by fiber to inter-connect most Central Offices (CO’s) in the United States at bit rates ranging from the SONET base rate of 51.84 Mbps up to 39,813,120 Gbps. 

The base SONET standard bit rate is 51.84 Mbps and is referred to as Optical Carrier  (OC) -1 or Synchronous Transport Level  (STS) -1. SONET uses a synchronous structure for framing that allows multiplexed pieces down to individual DS-0 channels to be pulled off a SONET signal without having to demultiplex the entire SONET signal. We can look at a table of SONET bit rates.

[The OC-3072 (160 Gbps) rate level is next in the sequence but has not yet been standardized.]

The OC-1 base is used for all higher level SONET specifications. For example, a SONET specification of OC-48 can be calculated by taking the OC-1 base rate of 672 DS-0 channels and multiplying it by the OC-48 suffix of 48.

We can do the same calculation for the OC-192 specification.

It is common to run SONET rings CO to CO with all SONET connected CO’s having SONET multiplexers that can demultiplex all the way down to an individual DS-0 channel level without having to demultiplex the entire SONET frame. 

In my next legacy post I'll take a look at how SONET is used for packet-oriented data transmission (e.g. Ethernet).

No T1 Lines in Europe - The E-Carrier Hierarchy

Today I'll continue with a post on what I've been calling the legacy Public Switched Telephone Network (PSTN). In my last legacy post we covered T-4 and T-5 lines, today let's take a look at the European or “E” carrier system.

The European or “E” digital transmission format is slightly different than the North American T-carrier system format. With the E-Carrier system we are still taking individual voice call analog signals and converting to a digital signal by sampling the analog signal 8000 times per second and, after matching the instantaneous voltage sample level to one of 256 discrete levels, generating an 8 bit code for each sample. We are still dealing with the fundamental DS-0 building block of 64Kbps of digital bandwidth per single analog voice channel we used for the T-Carrier system. The differences between E-Carrier and T-Carrier deals with the number of channels and how these channels are used. Let’s start by looking at a European E-1 system and how it compares to a North American T-1 system.

The E-Carrier system starts by multiplexing 32 DS-0 channels together to form an E-1 circuit while the North American T-Carrier system multiplexes 24 DS-0 channels to form a T-1 circuit. 

The 32 DS-0 channels of an E-1 circuit combine from Channel 0 up to Channel 31. Channel 0 is used for framing (synchronization), channels 1-15 and 17-31 are used for individual DS-0 channels and Channel 16 is reserved and not used.

This system is also referred to as the “30 plus 2 system” because an E-1 signal consists of 30 DS-0 signals used for voice plus Channel 0, which is used for overhead and Channel 16 which is not used at all. In the European system, all synchronization (framing) is handled by Channel 0 so framing bits are not required on individual DS-0 channels.

We can calculate the signal rate for an E-1 circuit as follows:

E-2 through E-5 are carriers in increasing multiples of the E-1 format. We can look at a table showing DS data rates and how they correspond to the European E Carrier system.

In my next legacy PSTN post I'll cover the Synchronous Digital Hierarchy (SDH) system.

DS-4 and DS-5 Lines

It's been a while since I've posted on what I've been calling the Legacy Public Switched Telephone Network (PSTN). My last related post was way back on December 15, 2011 titled What's a T3 Line? Today, Let's take a look at higher bit rate signals in the DS system.

DS-4 Signal
Back on December 15th, we said each DS-3 signal carries a bit rate of 44.736 Mbps. Six 44.736 Mbps digital DS-3 signals are multiplexed into one DS-4 signal. If we have six DS-3 signals per DS-4 signal and each DS-3 signal is 44.736 Mbps we can calculate:

Adding overhead consisting of timing and synchronization bits brings the DS-4 bit rate to 274.176 Mbps.

DS-4 Formation

DS-5 Signal

Each DS-4 signal carries a bit rate of 274.176 Mbps. Two 274.176 Mbps digital DS-4 signals are multiplexed into one DS-5 signal. If we have two DS-4 signals per DS-5 signal and each DS-4 signal is 274.176 Mbps we can calculate:

Adding overhead consisting of timing and synchronization bits brings the DS-5 bit rate to 560.16 Mbps.

DS-5 Formation

One DS-5 channel can carry 8064 voice channels.

We can look at a table showing these DS data rates and how they correspond to the North American T Carrier system.

Looking at the table it is easy to see that the DS-0 signal level is the foundation for the entire T Carrier hierarchy in North America. Notice one DS-1 line is the equivalent of 24 DS0 64 Kbps DS-0 voice channels. Also notice that one DS-2 line is the equivalent of 4 DS-1 lines or 96 DS-0 voice channels.

Copper wire pairs can be used to transmit at levels up to DS-2. At levels above DS-2 coaxial cable, fiber or microwaves must be used.

In my next Legacy PSTN post I'll cover the European (E) Carrier System.

What's a T3 Line?

In my last post I described what a T1, also called a DS-1, line was. Most of us have also heard the "T3 Line" term used. Let's take a look at what a T3 or DS-3 line is.

DS-2 Signal
Before we can describe a DS-3 line, let's first take a look at a DS-2. In that last post we figured out how each DS-1 signal (T1 line or circuit) carries a bit rate of 1.544 Mbps. Four 1.544 Mbps digital DS-1 signals are multiplexed into one DS-2 signal. If we have 4 DS-1 signals per DS-2 signal and each DS-1 signal is 1.544 Mbps we can calculate:

Adding overhead consisting of timing and synchronization bits brings the DS-2 bit rate to 6.312 Mbps.

DS-2 Formation

DS-3 Signal

Each DS-2 signal carries a bit rate of 6.312 Mbps. Seven 6.312 Mbps digital DS-2 signals are multiplexed into one DS-3 signal. If we have 7 DS-2 signals per DS-3 signal and each DS-2 signal is 6.312 Mbps we can calculate:

Adding overhead consisting of timing and synchronization bits brings the DS-3 bit rate to 44.736 Mbps.

And..... 44.736 Mbps.... that's a T-3 line!

T1 Lines - What They Are

Most of us have heard about "T1" lines. We know they are some kind of (expensive) communications line you can get from one of the telephone companies. It turns out T1's are part of the Digital Signal (DS) Level System. 

Back in August, I wrote a post titled More on CODECs: Quantization + Sampling Rate = A PCM Wave. In that post I described how a piece of an analog signal is quantized and companded and then given an 8 bit binary code in a process referred to as encoding. From that post, we know to convert an analog signal to a digital signal the analog signal is sampled 8000 times per second and, after matching the instantaneous voltage sample level to one of 256 discrete levels, an 8 bit code is generated for each sample. If we multiply the sample rate by the bit code we get:

(8000 samples/second)(8 bits/sample) = 64,000 bits per second (bps)

So we can say a single analog voice channel, after conversion from analog to digital, requires 64Kbps of digital bandwidth. This 64Kbps is referred to as Digital Signal Level 0 (DS-0) and is the basic building block or channel for the existing digitally multiplexed T carrier system in the United States and the digital E carrier system used in Europe. 

Voice calls are digitally multiplexed using either time division multiplexing or statistical time division multiplexing. Calls are grouped in a way similar to frequency division multiplexing. Let’s look at how this is done.

Digroups or DS-1 signals

Individual analog voice call channels converted to digital and require a bit rate of 64 Kbps each. 24 64 Kbps digital voice channels are multiplexed into digroups or DS-1 signals. If we have 24 DS-0 signals per DS-1 signal and each channel is 64 Kbps we can calculate:

Adding overhead consisting of timing and synchronization bits brings the DS-1 bit rate to 1.544 Mbps - that's a T1!

DS-1 Formation

DS-1 Overhead

We’ve described the process of encoding where an analog signal is sampled 8000 times per second, quantized into one of 256 discrete signal levels, companded it is then given an 8 bit binary code. After a single analog signal sample has been encoded it is multiplexed, with 24 other encoded 8 bit sample signals. This generates a 192 bit (8 bits/sample signal × 24 sample signals) sequence for the 24 sample signals. A process called framing then adds one framing bit to create a 193 bit frame.

DS-1 With Overhead

The framing bits are used to keep the receiving device in synch with the frames it is receiving. Every twelve frames are grouped into a masterframe, also referred to as a superframe. Included within each masterframe is a twelve bit frame pattern from the 12 grouped 193 bit frames This twelve bit frame pattern carries a bit pattern of 000110111001 and repeats itself with each masterframe.

Masterframe

This masterframe bit pattern is used for synchronization.

Remember each channel is sampled 8000 times per second so a single frame represents one eight-thousandth of 24 individual channels or telephone calls. We can also say that, in one second a DS-1 signal transmits 8000 193 bit frames. We can use these numbers to calculate the true DS-1 bit rate which includes both data and overhead (framing) bits:

Each DS-1 signal carries a bit rate of 1.544 Mbps and.... that's a T1!