# Question: In a digital communication system a block of data bits

In a digital communication system, a block of data bits is mapped into an - bit codeword that typically contains the information bits as well as n – k redundant bits. This is known as an (n, k) block code. The redundant bits are included to provide error correction capability. Suppose that each transmitted bit in our digital communication system is received in error with probability p. Furthermore, assume that the decoder is capable of correcting any pattern of t or fewer errors in an bit block. That is, if t or less bits in an n bit block are received in error, then the codeword will be decoded correctly, whereas if more than errors occur, the decoder will decode the received word incorrectly. Assuming each bit is received in error with probability p = 0.03, find the probability of decoder error for each of the following codes.

(a) (n, k) = (7, 4) t = 1

(b) (n, k) = (15, 7) t = 2

(c) (n, k) = (31, 16) t = 3

(a) (n, k) = (7, 4) t = 1

(b) (n, k) = (15, 7) t = 2

(c) (n, k) = (31, 16) t = 3

## Answer to relevant Questions

A roulette wheel consists of 38 numbers (18 are red, 18 are black, and 2 are green). Assume that with each spin of the wheel, each number is equally likely to appear. (a) What is the probability of a gambler winning if he ...Using mathematical induction, prove Corollary 2.1. Recall, Corollary 2.1 states that for M event A1, A2, AM which are mutually exclusive (i,e.,Ai ∩ Aj = Ф for all i ≠ j), Develop a careful proof of Theoram 2.1 which states that for any events A and B, Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B). One way to approach this proof is to start by showing that the set can be written as the union ...Repeat Exercise 3.1. A certain random variable has a probability density function of the form f x (x) = ce –2xu(x). Find the following: (a) The constant c, (b) Pr (X >2), (c) Pr (X < 3), (d) Pr (X < 3|X > 2). A Gaussian random variable has a PDF of the form Write each of the following probabilities in terms of Q- functions (with positive arguments) and also give numerical evaluations: (a) (X > 0), (b) (X > 2), (c) (X > –3), (d) ...Post your question