encoding - How to encode packet information by XOR in matlab -

encoding - How to encode packet information by XOR in matlab -

i working in channel coding part. major encoding bit information. example, given input bit x=[1 0 1] , g matrix

g = 1 0 0 1 0 0 1 0 1 1 0 1

then encoding symbol y=mod(x*g,2)% mod convert binary bit

y = 0 1 0 0

it simple thought bits encoding processing in channel coding. want map work packet encoding. paper mentioned can way packet encoding if consider each packet n bytes. example, have text file size 3000bytes. split file 1000 packet. hence, each packet has size 3 bytes. problem done bit encoding. however, don't have thought work packet encoding. please allow me know if worked problem. hear bit encoding has 2 level 0 , 1, can utilize gf=2. if work packet level, must consider gf>2. not sure second question how if packet size equals 50 bytes instead of 3 bytes?

first, when talk gf(p^m), mean galois field, p prime number indicates grade of polynomial. hence, possible define field pm elements. in case, p=2 , m=3. once, have polynomial, can apply using 2 different encoding schemes:

block coding. can split packet several blocks of 3 bits , encode each block independently. utilize zero-padding in case not multiples. convolutional coding. apply polynomial sliding algorithm.

the sec approach more robust , has lower delays.

the gf terminology used work polynomials, concepts of extended galois fields , polynomials not complicated, takes time understand it. however, in practice, if have polynomial look apply bit sequence in fashion want, block or convolutional (or fountain).

you matrix g defining 4 polynomials input x=[1 x x^2], namely y1=1+x^2, y2=x^2 , y3=x, y4=1+x^2

matlab encoding packet decoding