This document provides information and formulas related to information theory and coding. It discusses important cyclic codes like Reed-Solomon codes and convolution codes. For convolution codes, it provides the generator matrix formulas in the time and transform domains, showing how the output of the encoder is calculated from the input and generator matrix. It also gives the formulas for calculating the output polynomials from the input polynomial and generator polynomials in the transform domain approach.

1. INFORMATION THEORY AND
CODING
5th SEM E&C
JAYANTHDWIJESH H P M.tech (DECS)
Assistant Professor – Dept of E&C
B.G.S INSTITUTE OF TECHNOLOGY (B.G.S.I.T)
B.G Nagara, Nagamangala Tq, Mandya District- 571448

2. FORMULAS FOR REFERENCE
MODULE – 5 (Some Important Cyclic Codes and Convolution
Codes)
Chapter -1 Some Important Cyclic Codes
 Reed – Solomon (RS) codes
Chapter-2 Convolution Codes
Time domain approach
 The generator matrix G is given by

3.  Number of rows in [G] =L (one input)
 Number of rows in [G] =2L (two inputs)
 Number of columns in [G]= n(L+M)
 The output of the encoder is given by
[C] = [d][G]
Transform domain approach
 The output polynomials for the j(j=1,2,3…) adders are given by
𝑪𝒋
(x)= d(x) 𝒈𝒋
(x) for j=1, 2, 3….
 The output of the encoder is given by
C(X) = 𝑪(𝟏)
(𝑿 𝒏
) +X 𝑪(𝟐)
(𝑿 𝒏
) + 𝑿 𝟐
𝑪(𝟑)
(𝑿 𝒏
) +……………+𝑿 𝒏−𝟏
𝑪(𝒏)
(𝑿 𝒏
)