Probability Of Error Detection In 16 Symbols System

Published Date: 02 Nov 2017

CHAPTER 4

EXPERIMENTAL WORK

4.1 HIGH SPEED NETWORK: High-speed links are present everywhere in modern computing and routing. In a personal computer, for instance, they link the central processing unit to the memory, while in backbone routers thousands of such links interface to the crossbar switch. Arising from the critical tasks they are designed to perform, high-speed links are subject to stringent throughput, accuracy and power consumption requirements. A typical high-speed link operates at a data rate on the order of 10 Gbps with error probability of approximately 10−15.The block diagram of high speed network is drawn below:

Ni Encoder

Channel

Decoder

Demodulator

Modulator

Figure 4.1 Block diagram of high speed networking

4.2 EXISTING SYSTEM

Error-correction coding for 10 Gbps backplane: The application of Ethernet as a fabric technology in modular platforms has led to interest in the development of a standard set of physical layer subsystems to support this practice. Recently, the IEEE 802.3ap-2007 standard, commonly referred to as Backplane Ethernet, was approved. This standard defines the electrical performance of the backplane interconnect, transmitters and receivers required to support data rates up to 10 Gbps per channel. This paper provides an overview of the key specifications for serial 10 Gbps Backplane Ethernet and relates the requirements to backplane construction considerations and link performance trade-offs.

Error-correction coding in a serial digital multi-gigabit communication system: The analysis used in choosing and designing an error correction coding (ECC) scheme for a wired serial digital multi-gigabit communication system. Background information is provided on multi-gigabit systems, followed by a detailed analysis leading to an ECC design. The analysis consists of determining the transmission channel bandwidth, identifying the significant noise sources, using estimates of Eb/N0 to determine channel capacity, establishing the relevant characteristics of the source data, and determining for specified random and deterministic jitter levels the probability of a bit error vs. the sampling time point. These analyses are used to develop ECC requirements for the selection and design of the code. A two-error correcting BCH code is selected and specified. The target for implementation of the ECC design is an ALTERA STRATIX GX Field programmable gate array (FPGA). This family of FPGAs contains embedded serial transceivers that can operate at up to 3.125 Gbps. The ECC design in this paper included consideration of the capabilities of an FPGA implementation.

Disadvantages:

Lack of suitable analysis and simulation frameworks

Speed/reliability/ energy efficiency of the system, the technique remains unexploited in High-speed backplane and chip-to-chip interconnects.

Residual inter-symbol interference (ISI), coupled with noise and other circuit

impairments, significantly obscures the performance picture and renders both the

theoretical and computational approaches more arduous.

4. Ignore error correlation between symbols.

4.3 PROPOSED SYSTEM

Model the high-speed link as a system with additive white noise and ISI, makes it possible to describe the error correlation in terms of two fundamental quantities: the systems’ error region and the channel’s sign signature. The error region corresponds to the set of values in the ISI distribution that are responsible for the majority of errors. While the error region is determined by the combined noise and the magnitude of the coefficients forming the channel’s pulse response, the channel signature is specified by the signs of those coefficients. The analysis shows how these quantities conceptually decouple the complex problem of accounting for the effect of a real-valued channel on error behavior and provide a missing insight into error correlation in a high-speed link. While current statistical simulation techniques for high-speed links ignore error correlation between symbols, shows that a direct extension of the independent-errors approximation improves the estimate’s accuracy by up to five orders of magnitude for the error rates of interest. The approach exploits the physical properties of high-speed links, particularly the nature of the ISI, which limits the range of the error correlation. It relies on accurately capturing the short-term error correlation within non overlapping blocks of symbols and assumes independence in the error behavior across distinct blocks, rather than individual symbols. The computational mechanics are those of integer partitions and the approach is computationally efficient for high-speed link channels. The proposed analysis and simulation frameworks also present a case against the use of existing techniques in the performance estimation of coded high-speed links.

Advantages:

Energy-efficient channel coding to high-speed links

2. Direct extension of the independent-errors approximation improves the estimates

Accuracy by up to five orders of magnitude for the error rates of interest

3. Proposed analysis and simulation frameworks also present a realistic case

against use of existing approach.

4.4 MODULE EXPLANATION

Module 1: Designing the system model, in that we are simulating the channel impulse model, along with corresponding inter symbol interference distribution.

A simplified model of a high-speed link is shown in Figure 4.1 here, the bit stream, which can be coded or uncoded (unconstrained), is modulated to produce the equivalent symbol stream and transmitted over a communication channel. The system employs PAM2 modulation with detection performed on a symbol-by-symbol basis with the decision threshold at the origin. The transmitter and receiver may contain equalizers, in which case the channel’s impulse response may contain residual ISI. The two main mechanisms that account for the most significant portion of the residual ISI in high-speed links are dispersion and reflection. In addition, residual interference may also include co-channel interference, caused, for instance, by electro-magnetic coupling (crosstalk). As accounting for co-channel interference involves the same set of mathematical tools as accounting for the ISI.

The quantity of interest is the received signal at the input to the decision circuit at time, denoted and Yi expressed as

Yi= Zi+Ni

Zi denotes the received signal in the absence of noise

Ni denotes the noise term

In a coded system with ISI, this picture changes in two important ways. Due to constraints on the symbol stream, the marginal error probabilities are no longer equal across different symbols. An efficient method of computing for different symbol locations in a codeword is described in, which focuses on systematic binary linear block codes. However, the performance of a coded system cannot be expressed through marginal error statistics alone, but is instead dependent on the joint error behavior. For instance, the performance of a error correcting linear block code is typically expressed through the word error rate (WER), given by the probability of observing at least(t+1) errors in a codeword.

The following development shows that the complex relation between the ISI and the joint error behavior can be greatly elucidated by decoupling the effects of the magnitude and the signs of the channel’s pulse response. Understanding the effect of system’s error region and channel’s sign signature on error correlation ends a deeper insight into the behavior of codes and the shortcomings of common simulation techniques in high-speed links.

Figure4.2(a): Channel Pulse Response

Figure 4.2(b): ISI distribution

Module 2: Generating equalized pulse response for various channels named as Channel A, channel B

The communication channel of Fig. 4.3(a) is a standard channel operating at 10 Gb/s. In this step we have used two different channels for seeing the pulse response. The channel of Fig. 4(b) is obtained by altering the signature of the original channel, which preserves the marginal error behavior, but alters the joint error statistics. As we can see both have different characteristics in time domain.

Figure 4.3(a) Equalized pulse response of channel A

Figure 4.3(b) Equalized pulse response of channel B

Module 3: Simulation of Proposed Work

The work is simulated in Maltab 7.8. In this work we have performed the implementation on different network to different respective number of symbols in network. Data bit is transmitted over the channel. The work is implemented for 4 symbol, 6 symbol, 10 symbol and 16 symbol networks. The work is implemented on the receiver side. For each set of symbol data bit is transmitted independently. At the receiver end error is detected for each block. Different number of symbol in the network represents different error.

Module 4: Comparative Analysis

Finally the results are analyzed by performing the comparison of presented approach with some existing approach. The results are presented graphically. Both the existing and proposed approach is implemented on same network and with same network properties. As the data is transmitted over the network it is evaluated and analyzed by using both existing and proposed approach. The comparison is performed in terms of efficiency and the reliability of the error detection.

CHAPTER 5

RESULT AND DISCUSSION

5.1 SIMULATION ENVIRONMENT

MATLAB is a high-level technical computing language and interactive environment for algorithm development, data visualization, data analysis, and numeric computation. Using the MATLAB product, you can solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran. You can use MATLAB in a wide range of applications, including signal and image processing, communications, control design, test and measurement, financial modeling and analysis, and computational biology. Add-on toolboxes (collections of special-purpose MATLAB functions, available separately) extend the MATLAB environment to solve particular classes of problems in these application areas. MATLAB provides a number of features for documenting and sharing your work. You can integrate your MATLAB code with other languages and applications, and distribute your MATLAB algorithms and applications.

5.2 MATLAB FEATURES

• High-level language for technical computing

• Development environment for managing code, files, and data

• Interactive tools for iterative exploration, design, and problem solving

• Mathematical functions for linear algebra, statistics, Fourier analysis, filtering, optimization, and numerical integration

• 2-D and 3-D graphics functions for visualizing data

• Tools for building custom graphical user interfaces

• Functions for integrating MATLAB based algorithms with external applications and Languages, such as C, C++, FORTRAN, Java™, COM, and Microsoft® Excel®

MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

Typical uses include:

• Math and computation

• Algorithm development

• Modeling, simulation, and prototyping

• Data analysis, exploration, and visualization

• Scientific and engineering graphics

• Application development, including Graphical User Interface building

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C or FORTRAN. The name MATLAB stands for matrix laboratory. MATLAB was originally written to provide easy access to matrix software developed by the LINPACK and EISPACK projects, which together represent the state-of-the-art in software for matrix computation.

MATLAB has evolved over a period of years with input from many users. In university environments, it is the standard instructional tool for introductory and advanced courses in mathematics, engineering, and science. In industry, MATLAB is the tool of choice for high-productivity research, development, and analysis.

MATLAB features a family of application-specific solutions called toolboxes. Very important to most users of MATLAB, toolboxes allow you to learn and apply specialized technology. Toolboxes are comprehensive collections of MATLAB functions (M-files) that extend the MATLAB environment to solve particular classes of problems. Areas in which toolboxes are available include signal processing, control systems, neural networks, fuzzy logic, wavelets, simulation, and many others.

5.3 SIMULATION RESULTS

In this section the results obtained from the proposed system are presented and analyzed.

Figure 5.1: Data Bits Transmitted over the channel

As we can see in figure 5.1, the data bits transmitted over the channel in a block of 4 symbol each. The lines here show data 1 and the blue circles shows the 0 value.

Figure 5.2: Subplot of the data channel of 4 symbol

As we can see in figure 5.2, the previous fig 5.1 is drawn as subplot. The Error is detected in each block of dataset independently. As we can see each block is of 4 symbols. Each block detects different number of errors by comparing at the receiver end.

Figure 5.3: Data Bits Transmitted over the channel

As we can see in figure 5.3, the data bits transmitted over the channel in a block of 6 symbol each. The lines here show data 1 and the blue circles shows the 0 value.

Fig 5.4: Subplot of the data channel of 6 symbol

As we can see in figure 5.4, the previous fig 5.3 is drawn as subplot .The Error is detected in each block of dataset in case of 6 symbol dataset independently. Each Block detects different number of errors by comparing at the receiver end.

Figure 5.5: Data Bits Transmitted over the channel

As we can see in figure 5.5, the data bits transmitted over the channel in a block of 10 symbol each. The lines here show data 1 and the blue circles shows the 0 value.

Figure 5.6: Subplot of the data channel of 10symbol

As we can see in figure 5.6, the previous figure (5.5) is drawn as subplot. The Error is detected in each block of dataset in case of 10 symbol dataset independently. Each Block detects different number of errors by comparing at the receiver end.

.

Figure 5.7: Data Bits Transmitted over the channel

As we can see in figure 5.7, the data bits transmitted over the channel in a block of 16 symbol each. The lines here show data 1 and the blue circles shows the 0 value.

Figure 5.8: Subplot of the data channel of 16 symbol

As we can see in figure 5.8, the previous fig (5.7) is drawn as subplot. The Error is detected in each block of dataset in case of 16 symbol dataset independently. Each Block detects different number of errors by comparing at the receiver end.

0

0.5

1

1.5

2

2.5

3

3.5

4

10

-2

10

-1

10

0

Es/No, dB

probablity

Probability of observing k errors in block of 4 symbols

Existing Approach

monte carlo

Figure 5.9: Probability of Error Detection in 4 Symbols System (Existing Vs. Proposed)

As we can see in figure 5.9, the X-Axis represents the Error in the channel and Y axis represents the probability of detection of error. As we can see the detection chances of error is same and somewhat decrease in case of existing approach but the proposed system gives the better ratio of error detection chances.

Figure 5.10: Probability of Error Detection in 6 Symbols System (Existing Vs. Proposed)

As we can see in figure 5.10, the X-Axis represents the Error in the channel and Y axis represents the probability of detection of error. As we can see the detection chances of error is somewhat decrease in case of existing approach but the proposed system gives the better ratio of error detection chances.

0

1

2

3

4

5

6

7

8

9

10

10

-2

10

-1

10

0

Es/No, dB

probablity

probablity of observing k errors in a block of 10 symbols

Existing Approach

monte carlo

Figure 5.11: Probability of Error Detection in 10 Symbols System (Existing Vs. Proposed)

As we can see in figure 5.11, the X-Axis represents the Error in the channel and Y axis represents the probability of detection of error. As we can see the detection chances of error is somewhat decrease in case of existing approach but the proposed system gives the better ratio of error detection chances.

Figure 5.12: Probability of Error Detection in 16 Symbols System (Existing Vs. Proposed)

As we can see in figure 5.12, the X-Axis represents the Error in the channel and Y axis represents the probability of detection of error. As we can see the detection chances of error is decreasing in case of existing approach but the proposed system gives the better ratio of error detection chances.

CHAPTER 6

CONCLUSION AND FUTURE WORK

6.1 CONCLUSION

The presented work is the implementation of improved Monte Carlo Approach to perform the channel encoding for high speed network. The work is independent to the network type. It can be implemented on any high speed Gigabit network such as PON. The presented approach is encoding scheme that is improved using Monte Carlo approach. The comparative analysis is also performed with some existing approach that shows the presented approach is far efficient and reliable the existing approach. We have implemented the work for 4 symbol , 6 symbol, 10 symbol and 16 symbol networks. The obtain results shows the presented work is better in all these formats.

6.2 FUTURE WORK

In this presented work an efficient and reliable encoding scheme is suggested for high speed network. The obtained results show that the presented work is being performed effectively for the network. But still there is the scope of some more improvement over the communication. Some of these improvements include

The work can be tested on different kind of network under different transmission schemes and different modulation schemes.

We can improve the work to find the kind of error over the transmission.