Question

You are streaming a five-minute video and receive \(80 \mathrm{Mbps}\) of encoded data per second, with a compression ratio of \(200: 1\). The video has a resolution of \(2000 \times 1000\) pixels, uses 20 bits per pixel, and is played at 60 frames per second. After \(40 \mathrm{sec}\)., your Internet connection breaks down. Can you watch the video to completion?

Short answer

No, you cannot watch the video to completion after the internet disconnection.

Step-by-step solution

Determine Total Data Received

Calculate the total data received in 40 seconds: \[ 80 \text{ Mbps} \times 40 \text{ seconds} = 3200 \text{ Mb} \]

Calculate Uncompressed Data Size per Second

The uncompressed data rate is given by the formula: \[ \text{Uncompressed data rate} = \text{compression ratio} \times \text{received data} \]Given the compression ratio of 200:1, the uncompressed data per second is:\[ 200 \times 80 \text{ Mbps} = 16000 \text{ Mbps} \]

Calculate Video Bitrate

Find the total bits per frame based on resolution and bits per pixel:\[ 2000 \times 1000 \times 20 = 40,000,000 \text{ bits per frame} \]For 60 frames per second, the video's bitrate is:\[ 40,000,000 \times 60 = 2,400,000,000 \text{ bits per second} = 2400 \text{ Mbps} \]

Calculate Total Data Needed for the Video

The total data needed for a 5-minute video is calculated by:\[ 2400 \text{ Mbps} \times 300 \text{ seconds} = 720,000 \text{ Mb} \]

Determine Viewable Duration with Received Data

Calculate how much of the video can be watched with 3200 Mb of uncompressed data received:\[ \text{Time viewable} = \frac{3200 \text{ Mb}}{2400 \text{ Mbps}} = \frac{3200}{2400} \text{ seconds} = \frac{4}{3} \text{ seconds} \]

Conclude Whether Video Completes

Since you only have enough data to watch \( \frac{4}{3} \) seconds of the video after the internet disconnects, you cannot watch the entire video after the first 40 seconds.

Key concepts

Compression Ratio

In video streaming, the compression ratio is a critical factor that determines how much the original video data can be reduced in size for efficient transmission and storage. A compression ratio is expressed as a ratio, such as 200:1, meaning that the original data size is reduced by 200 times. For example, if a video is compressed at a 200:1 ratio, this means that the resulting file is significantly smaller than the uncompressed file, allowing for quicker transmission over networks.
This process ensures that videos can be streamed smoothly without requiring excessive bandwidth. Video compression utilizes algorithms to remove redundant data without significantly compromising quality. It is essential in keeping file sizes manageable while maintaining the integrity of the data being viewed.

Data Rate Calculation

Data rate calculation in video streaming refers to determining the amount of data that is being transferred every second. It is usually measured in megabits per second (Mbps). The data rate can help assess the quality and smoothness of video playback.
To calculate it, multiply the compressed data rate by the time duration. For example, if you receive 80 Mbps for 40 seconds, you calculate this as:

• Received data = 80 Mbps × 40 seconds = 3200 Mb

Understanding the data rate is crucial for ensuring that your network can handle the video stream without interruptions or quality loss. Additionally, the data rate can determine the amount of buffer required in case of network disruptions.

Frames Per Second

Frames per second (fps) is an important aspect of video streaming, as it determines how many individual images, or frames, are displayed each second in a video. A higher fps means smoother motion in the video. Common frame rates include 24 fps for cinematic films, 30 fps for TV shows, and 60 fps for high-definition video and gaming.
For our example video, the frame rate is 60 fps. This high frame rate ensures fluid motion, which is especially beneficial for dynamic scenes such as action sequences or sports broadcasts. The choice of frame rate affects both the perceptual quality and the video file size – higher fps requires more data.

Video Bitrate

Video bitrate defines the amount of data processed over a given time in a video stream. Measured in Mbps, it indicates both the quality of the video and the required bandwidth. A higher bitrate generally implies better video quality and requires more bandwidth for smooth streaming.
To calculate the bitrate, use the formula considering the frame size and frames per second. For instance, with a 2000 × 1000 resolution and 20 bits per pixel at 60 fps, calculate as follows:

• Bits per frame = 2000 × 1000 × 20 = 40,000,000 bits per frame
• Video bitrate = 40,000,000 bits/frame × 60 frames/second = 2,400,000,000 bits/second = 2400 Mbps

This calculation helps determine both the storage requirements and streaming capabilities necessary to deliver the desired video quality efficiently.