Question

What is the compression ratio needed to send a \(4 \mathrm{~K}\) video over a \(80 \mathrm{Mbps}\) channel? Assume that the video plays at a rate of 60 frames per second, and every pixel value is stored in 3 bytes.

Short answer

The compression ratio needed is approximately 149.3.

Step-by-step solution

Calculate Resolution of 4K Video

A 4K video resolution is typically 3840 pixels by 2160 pixels. To find the total number of pixels per frame, multiply these values:\[3840 \times 2160 = 8,294,400 \text{ pixels per frame}\]

Calculate Data Size per Frame

Each pixel is stored in 3 bytes, so multiply the total number of pixels by 3 to get the data size per frame:\[8,294,400 \times 3 = 24,883,200 \text{ bytes per frame}\]

Convert Frame Data Size to Bits

Since 1 byte is equal to 8 bits, convert the bytes into bits:\[24,883,200 \times 8 = 199,065,600 \text{ bits per frame}\]

Calculate Total Data Rate Without Compression

The video plays at 60 frames per second, so multiply the data size per frame by the frame rate to find the total data rate:\[199,065,600 \times 60 = 11,943,936,000 \text{ bits per second}\]

Determine Required Compression Ratio

To send the data over an 80 Mbps channel, divide the data rate without compression by the channel's capacity to find the required compression ratio:\[\frac{11,943,936,000}{80,000,000} \approx 149.3\]

Conclusion on Compression Ratio

The compression ratio needed to send a 4K video over an 80 Mbps channel is approximately 149.3.

Key concepts

4K Video Resolution

4K video resolution is a term that represents a high-definition video format. It generally means that the video has a resolution of 3840 x 2160 pixels. This is approximately four times the resolution of typical high-definition (HD) resolution, which is 1920 x 1080 pixels. As the name suggests, 4K resolution involves around 4,000 pixels horizontally, hence '4K'.
Each frame at this resolution comprises a large number of pixels—specifically, 8,294,400 pixels per frame. This high pixel count allows for incredibly detailed and sharp video quality, making it a popular choice for cinema and streaming platforms looking to provide the utmost in picture clarity. More pixels mean richer detail, which closely echoes real-life viewing experience. However, this also leads to increased data sizes and necessitates consideration of efficient data storage and transmission methods.

Video Frame Rate

The video frame rate refers to the frequency at which consecutive images, known as frames, appear on a display screen. Frame rate is expressed in frames per second (fps).
A common frame rate for video playback is 30 fps, but for smoother and more realistic motion, 60 fps is often preferred, especially in sports and action footage. This means that every second, the video displays 60 individual frames, which can considerably enhance the viewer's experience by providing smoother transitions and less motion blur.

• More frames per second generally mean larger data requirements due to the number of images being processed each second.
• Higher frame rates can also utilize more processing power and bandwidth when streaming over the internet.

In the context of 4K video, maintaining a high frame rate, such as 60 fps, results in exceptional video quality but requires efficient data management techniques to handle the influx of data.

Pixel Data Storage

In digital imaging, pixel data storage is crucial for determining the quality and size of the video files. Each pixel in a frame stores information about the color and brightness of a specific part of the image. In the context of 4K video, each pixel value is often stored in 3 bytes.
These 3 bytes could represent different components of color, usually red, green, and blue (RGB). Each color component takes up one byte, allowing for 256 levels of intensity for each color. Multiplied across millions of pixels in a single frame, the storage requirement grows significantly, resulting in large file sizes for high-resolution video frames.
Properly compressing this pixel data without drastically reducing quality is a major challenge in video storage solutions and streaming services. Transmitting such data over limited-bandwidth internet connections requires sophisticated compression techniques to manage the heavy pixel data effectively.

Bit Rate Calculation

Bit rate calculation involves determining how much data is processed for a given video, typically expressed in bits per second (bps).
To calculate the required bit rate for a video, you multiply the following:

• The number of pixels per frame
• The size of each pixel in bits
• The number of frames per second

In our original exercise, this calculation leads to understanding the sheer volume of data that needs to be transferred — with over 199,065,600 bits needed just for one frame at 4K and 60 fps!
The total video data rate without compression was found by multiplying this frame size by the frame rate (60 fps), resulting in about 11,943,936,000 bits per second. To stream such rich content over an 80 Mbps channel, determining an efficient compression ratio becomes crucial to ensure smooth transmission with minimal loss of quality.