DIGITAL SYTEM DESIGN MINI PROJECT CONVOLUTION CODES PRESENTED BY:- PRATEEK ATLANI 6449 PRATIK AGARWAL 6450 PUNEET MANN 6451 VISHNU VARDHAN 6452

DATA TRANSFER :- SERIAL COMMUNICATIONS PARALLEL COMMUNICATIONS PROBLEMS:- Noise Electronic devices malfunctioning. Hazards caused by noise NOISE REMOVAL METHODS:- 1.Addition of correction bits 2.Code conversion using different techniques

Convolution codes is one of best methods for data transfer in serial communications Basic operations:- 1.Encoding 2.Decoding ENCODING:- In this we convert a given code to another one with some additional bits added. DECODING:- The encoded output is fed to give us back the Message signal.

Problem statement: Implement the following convolution code (encoding and decoding) on FPGA using vhdl . The code (m,n,k) is (2,2,3). ENCODING:-The encoder is a finite state machine that consists of a M stage shift register with prescribed connections to n modulo 2-adders and a multiplexer that serializes the outputs of the adders. The constraint length of a convolution code is the number of shifts over which a single message bit can influence the encoder output In M stage shift register constraint length k =M+1

One input bit gives two output bits for one clock

Consider a message signal (101100) The polynomial representation of message signal =1+D^2+D^3 Where D represents unit delay variable Generator polynomial for path1 =1 Generator polynomial for path2 = 1+D+D^2 Therefore the O/p polynomial of path 1 is (1+D^2+D^3)X1=1+D^2+D^3 The o/p polynomial for path2 is (1+D^2+D^3)X(1+D+D^2)=1+D+D^5 The encoded sequence will have a length of n(L+K-1)=2X(6+3-1)=16 Therefore the O/p sequence is (11,01,10,10,00,01,00)

The shift register to be restored to its initial state , a terminating sequence of k-1 zeroes is appended to the last bit of the message sequence .These terminating sequence of zeroes is called tail of the message. The total 8 clock pulses are required so the o/p carrier wave contains 8X2=16 bits It gives the total of 16 bits Encoding can be done in three ways 1.Code tree 2.State machine Using state machine method encoding is realised in vhdl coding using state analysis

State Register A Register B S0 S1 1 S2 S3

o/p using this method also comes as (11,01,10,10,00,01,00) the output of the encoder will be 16 bits with the first two bits(k-1) being zeroes. Therefore the carrier wave sequence is 00,11,01,10,10,00,01,00 DECODING:- The output is 6 bits because we are considering the message width of 6 bits to the encoder. In this we use viterbi algorithm which uses trellis diagram for finding out the maximum likelihood decoder output . The reason for choosing trellis diagram is that the number of nodes does not continue to grow as the message bits increases.

TRELLIS DIAGRAM FOR DECODING PURPOSE

We observe at level 5 ,there are two paths entering each node We observe at level 5 ,there are two paths entering each node. Minimum distance decoder may make a decision at that point as to which of those two paths to take . this sequence goes on… The algorithm operates by computing a discrepancy for every possible path in the trellis The discrepancy for a path is defined as the hamming distance between the coded sequence and the received sequence. The path with the lower discrepancy is retained. The paths retained are called survivor paths. If the survivor paths are equal then we made a guess to decide the correct output .In the code all possible survivor paths are displayed Max number of survivor paths is given by 2^(k-1).

BACKGROUND ROOTS OF THE PROJECT LIES IN SHANNON’S INFORMATION THEOREM: IT SAYS THAT HOW MUCH NOISE THE CHANNEL MAY BE IT IS POSSIBLE TO GET THE DATA TRANSFERRED.

BACKGROUND CODE RATE:WHAT PORTION OF TOTAL AMOUNT OF DATA TRANSFERRED IS USEFUL. IN CASE OF OUR PROJECT IT IS NEARLY 0.90 METHODS FOR CHOOSING ERROR CORRECTING CODES. DEPENDS UPON EXPECTED ERROR RATE. WE CAN ADOPT COMPLEX SCHEMES FOR FASTER SYSTEMS LIKE EMBEDDED SYSTEMS.

BANDWIDTH(LENGTH OF CODE), CODING DELAY,CODING COMPLEXITY. THESE CODES ARE USED IN SPACE COMMUNICATION AND DEEP SPACE COMMUNICATION. ADVANTAGES: IT IS COMPLICATED TECHNIQUE BUT IT IS USED POWERFUL CORRECTING CAPABILITY. SINCE IT IS HAVING HIGH BANDWIDTH SO IT IS USED AS IT IS FASTER TECHNIQUE, EXPECTED ERROR RATE IS LOW.