Self Correcting Message System
using Hamming Code

Table of Contents

• Table of Contents
• Abstract
• Description
  • Thought / Concept
• Circuit Design & Waveform
  • Self Correcting Message System
  • 1. Window Comparator
  • 2. XNOR of Window Comparator Inverted output
  • 3. Frequency Divider and pulse generator
  • 4. Hamming Code Encoder
  • 5. Hamming Code Decoder
• Software Tools Used
• Acknowlegdements
  • Social media IDs

Abstract

This paper presents, how to send a self-correcting message with the help of hamming code. Hamming code is an error detection and correction technique. Message bits are received in signal form and then check if there any bits get flipped due to noise and if is so then message get corrected by itself. Self-correcting message applies its 5 extended parity bits to check for each 11-bit data. If one bit get flipped, then that error bit is identified and corrected by this system, and if 2 bits get flipped then machine is able to detect that 2 errors are present. This system can be also used in Compact Disc (CD) and Digital Versatile Disc (DVD)

Description

Self-Correcting message system works for each 11 bits data which are further converted to 16 bits which includes 4 bits for redundancy for parity check and 1 bit is extended parity check. In this design, even parity is considered that is number of 1’s in data bits is even. Before transmitting the data, parity bits are generated for each 11 bit of data and transmits the 16 bits of data. And after transmission some checks are performed and which can be used for correcting any errors.

Thought / Concept

Click here to see images of the creation of the idea

1. Extended Hamming Code Technique for (15+1,11)
For creation of the algorithm or logic behind the Extended Hamming Code with 11 data bits and 4 parity bit checks on 11 data bits along with 1 one complete parity matrix approach is used

2. Circuit Design Approach

Circuit Design & Waveform

Self Correcting Message System

1. Window Comparator

Circuit Diagram

Input Waveform

Output Waveform

2. XNOR of Window Comparator Inverted output

Circuit Diagram

Output Waveform

Verilog Code for Inverter

Click Here to see Program File

module vinayak_inverter(output Y, input A);
   not (Y, A);
endmodule

3. Frequency Divider and pulse generator

Circuit Diagram

Output Waveform

Verilog Code for Frequency_Divider

Click Here to see Program File

module vinayak_frequency_divider ( clk,out_clk );

output out_clk;

input clk ;

reg [2:0]m;

initial m = 0;

always @ (negedge (clk)) begin
m <= m + 1;
end

assign out_clk = m[2];

endmodule

4. Hamming Code Encoder

Explanation

Hamming Code Encoder Block is created using verilog Code.
Inputs provided for this encoder is as follows

1. Inverted Window Comparator 2nd Opamp Output
2. Constant 0 bit
3. XNOR Output
4. Inverted Window Comparator 2nd Opamp Output
5. Frequency Divider by 8 Output
6. Inverted Window Comparator 1st Opamp Output
7. Clock Pulse
8. Inverted Window Comparator 1st Opamp Output
9. XNOR Output
10. Frequency Divider by 8 Output
11. Constant 0 bit

Output of Hamming Code Encoder is as follows

1. Constant 0 bit
2. Frequency Divider by 8 Output
3. XNOR Output
4. Inverted Window Comparator 1st Opamp Output
5. Clock Pulse
6. Inverted Window Comparator 1st Opamp Output
7. Frequency Divider by 8 Output
8. Inverted Window Comparator 2nd Opamp Output
9. XNOR Output
10. Constant 0 bit
11. Inverted Window Comparator 2nd Opamp Output
12. Extended Hamming COde Parity Bit
13. 1st Parity bit
14. 2nd Parity Bit
15. 3rd Parity Bit
16. 4th Parity Bit

Circuit Diagram

Output Waveform

Verilog Code for Hamming Code Encoder

Click Here to see Program File

module vinayak_hamming_ecoder(
    input [10:0] data_in,
    output [10:0] data_out,
    output p0, output p1, output p2, output p3, output p4
    );
        
    wire p_0,p_1,p_2,p_3,p_4;
    
    assign p_1 = data_in[0] ^ data_in[1] ^ data_in[3] ^ data_in[4] ^ data_in[6] ^ data_in[8] ^ data_in[10];
    assign p_2 = data_in[0] ^ data_in[2] ^ data_in[3] ^ data_in[5] ^ data_in[6] ^ data_in[9] ^ data_in[10];
    assign p_3 = data_in[1] ^ data_in[2] ^ data_in[3] ^ data_in[7] ^ data_in[8] ^ data_in[9] ^ data_in[10];
    assign p_4 = data_in[4] ^ data_in[5] ^ data_in[6] ^ data_in[7] ^ data_in[8] ^ data_in[9] ^ data_in[10];
    assign p_0 = data_in[0] ^ data_in[1] ^ data_in[2] ^ data_in[3] ^ data_in[4] ^ data_in[5] ^ data_in[6] ^ data_in[7] ^ data_in[8] ^ data_in[9] ^ data_in[10] ^ p_1 ^ p_2 ^ p_3 ^ p_4 ;

    assign data_out = {data_in};
    assign p0 = p_0;
    assign p1 = p_1;
    assign p2 = p_2;
    assign p3 = p_3;
    assign p4 = p_4;
endmodule

5. Hamming Code Decoder

Explanation

Hamming Code decoder give output as a original data bits wrt parity bits received with data bits. Input bits for Hamming Code decoder bloack is output bits of Hamming Code Encoder Block. Hamming COde Decoder Circuit Block give output as follows:

• Is error bit is present or not
• All parity bits which are calculated from input data bit and parity bit
• Original Data bits if one bit is corrected among 11 data bit

Circuit Diagram

Output Waveform

Verilog Code for Hamming Code Decoder

Click Here to see Program File

module vinayak_hamming_decoder(
    input [15:0] data_in,
    output parity,
    output [3:0] p,
    output [10:0] data
    );

    assign p[0] = data_in[1] ^ data_in[3] ^ data_in[5] ^ data_in[7] ^ data_in[9] ^ data_in[11]  ^ data_in[13]  ^ data_in[15];
    assign p[1] = data_in[2] ^ data_in[3] ^ data_in[6] ^ data_in[7] ^ data_in[10] ^ data_in[11] ^ data_in[14] ^ data_in[15];
    assign p[2] = data_in[4] ^ data_in[5] ^ data_in[6] ^ data_in[7] ^ data_in[12] ^ data_in[13] ^ data_in[14] ^ data_in[15];
    assign p[3] = data_in[8] ^ data_in[9] ^ data_in[10] ^ data_in[11] ^ data_in[12] ^ data_in[13] ^ data_in[14] ^ data_in[15];
    assign parity = data_in[0] ^ data_in[1] ^ data_in[2] ^ data_in[3] ^ data_in[4] ^ data_in[5] ^ data_in[6] ^ data_in[7] ^ data_in[8] ^ data_in[9] ^ data_in[10] ^ data_in[11] ^ data_in[12] ^ data_in[13] ^ data_in[14] ^ data_in[15];
    
    assign data[0] = data_in[3];
    assign data[1] = data_in[5];
    assign data[2] = data_in[6];
    assign data[3] = data_in[7];
    assign data[4] = data_in[9];
    assign data[5] = data_in[10];
    assign data[6] = data_in[11];
    assign data[7] = data_in[12];
    assign data[8] = data_in[13];
    assign data[9] = data_in[14];
    assign data[10] = data_in[15];

endmodule

Software Tools Used

1. eSim

eSim is a free and open-sourced EDA tool for circuit design, simulation, analysis and PCB design. It is an integrated tool built using free/libre and open source software such as KiCad, Ngspice, Verilator, makerchip-app, sandpiper-saas and GHDL. eSim is released under GPL.

2. KiCad

KiCad's Schematic Editor supports everything from the most basic schematic to a complex hierarchical design with hundreds of sheets. It helps to create our own custom symbols or use some of the thousands found in the official KiCad library. We can verify our design with integrated SPICE simulator and electrical rules checker.

3. Ngspice

Ngspice is a mixed-level/mixed-signal electronic circuit simulator. Ngspice implements three classes of analysis: nonlinear DC analyses, Nonlinear transient analyses, linear AC analyses.

4. Verilator

Verilator is a free and open-source software tool which converts Verilog code to a cycle-accurate behavioral model in C++ or SystemC.

5. Makerchip

A web-based IDE that is used to design and simulate digital circuits using Verilog, and the language extension of Verilog, TL-Verilog.

6. SkyWater KY130 PDK

The SkyWater Open Source PDK is a collaboration between Google and SkyWater Technology Foundry to provide a fully open source Process Design Kit and related resources, which can be used to create manufacturable designs at SkyWater’s facility.

Note : Click on Drop Down Arrow to know more about software or click on software name to visit offical website

Acknowlegdements

1. FOSSEE, IIT Bombay
2. Kunal Ghosh, Co-founder, VSD Corp. Pvt. Ltd. - Email
3. Sumanto Kar, eSim Team, FOSSEE
4. Spoken Tutorial
5. Chips to Startup (C2S)
6. Google

Social media IDs

SPOKEN TUTORIAL: https://spoken-tutorial.org/
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TWITTER: https://twitter.com/FOSSEE/
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