Question

Suppose that an 11-Mbps \(802.11 \mathrm{~b}\) LAN is transmitting 64-byte frames back-lo-back over a radio channel with a bit error rate of \(10^{-7}\). How many frames per second will be damaged on average?

Short answer

On average, approximately 11 frames are damaged per second.

Step-by-step solution

Calculate the Number of Bits per Frame

First, let's determine the number of bits in a single frame. Each byte consists of 8 bits, so a 64-byte frame contains \(64 \times 8 = 512\) bits.

Determine the Probability of a Frame Being Damaged

The probability of a bit being in error is given to be \(10^{-7}\). Since a frame is damaged if at least one bit is erroneous, we calculate the probability of no errors in a frame as \( (1 - 10^{-7})^{512} \).

Calculate the Probability of a Frame Being Damaged

The probability of a frame being damaged is the complement of no errors occurring in a frame. Thus, \( P( ext{frame is damaged}) = 1 - (1 - 10^{-7})^{512} \). Using the approximation for small \(p\) values, \( (1-p)^n \approx 1-np \) when \( np \) is very small, we have \( 1 - 512 \times 10^{-7} \). So, the probability a frame is damaged is approximately \( 512 \times 10^{-7} \).

Calculate the Transmission Rate in Frames per Second

The transmission rate of the network is 11 Mbps. To find out how many frames are transmitted per second, we divide 11,000,000 bits per second by 512 bits per frame, giving \( \frac{11,000,000}{512} \approx 21,484 \) frames per second.

Calculate the Average Number of Damaged Frames per Second

The average number of frames damaged per second is the total frames transmitted per second multiplied by the probability of a frame being damaged. Thus, it's \( 21,484 \times 512 \times 10^{-7} \approx 11.0 \) damaged frames per second.

Key concepts

802.11 standards

The 802.11 standards define the technical specifications for implementing wireless local area network (WLAN) communications. Under the umbrella of the IEEE (Institute of Electrical and Electronics Engineers), these standards represent different protocols meant for wireless networking. For instance, 802.11b, as used in the mentioned problem, was one of the first standards, established in 1999, that provided a data rate of up to 11 Mbps in the 2.4 GHz band.
Each new iteration of the standard aimed to improve aspects such as speed, range, and reliability. For example, later standards like 802.11g and 802.11n have managed to significantly increase the data rates and accommodate a broader range of networking requirements. These standards are essential for ensuring interoperability between various devices and seamless communication in wireless networks.
Understanding these protocols, like 802.11b, helps in grasping their role in the transmission and reception of data in wireless environments, impacting both speed and the nature of possible errors encountered.

Bit Error Rate

The bit error rate (BER) is a key measure of performance for any wireless communication system. It represents the rate at which errors occur in a communication network.
BER is defined as the ratio of incorrect bits received to the total number of bits sent during a specified time interval. In the given exercise, the BER is specified as \(10^{-7}\), indicating that, on average, one bit out of every 10 million bits will be erroneous during transmission.

• A lower BER signifies a more reliable transmission with fewer errors, while a higher BER indicates less reliable communication.
• BER is influenced by several factors, including the quality of the transmission medium, the power of the transmitting signal, and any interference encountered during transmission.

The importance of BER lies in its ability to impact overall network performance and the quality of data received by users. Understanding the BER can help in identifying and mitigating issues that degrade the performance of wireless networks.

Frame Transmission

Frame transmission is a fundamental concept in wireless networks, referring to the process of sending data in structured units known as frames. Frames are packets of data formatted according to network protocol standards, in this case, 802.11b.
A frame typically contains headers and payload data; the headers include necessary information such as the destination address and error-checking details. In the given problem, the frame size is 64 bytes, equivalent to 512 bits.

• During transmission, each frame is subject to potential error, as indicated by the bit error rate.
• The likelihood of a frame being damaged is correlated with the frame's length and the network's BER.

Understanding how frames are transmitted helps in the design and optimization of network protocols to ensure efficient, reliable communication. Successful frame transmission ensures data integrity and user satisfaction in a network.

Network Performance

Network performance is an overarching term that encompasses various metrics used to evaluate the efficacy and reliability of a network. It includes considerations like data rates, latency, frame error rates, and bit error rates.
In this exercise, network performance is exemplified by how many frames can be successfully transmitted per second without errors in a wireless network following the 802.11b standard.

• The transmission rate, as calculated, is approximately 21,484 frames per second at 11 Mbps.
• Given the BER, the problem illustrates that approximately 11 frames per second are damaged, impacting overall network performance.
• Other factors affecting performance include network congestion, signal strength, and environmental interference.

Improving network performance typically involves enhancing these factors, employing error correction techniques, and optimizing network protocols to maintain the integrity and speed of data transmission. Understanding network performance challenges engineers to innovate and improve upon existing technology to provide seamless and efficient communication solutions.