Question: Consider a systematic (8.4) code whose parity equations are: r p0 = al + a2 + a3 p1 = a0 + al + a2 p2

Consider a systematic (8.4) code whose parity equations are: r

p0 = al + a2 + a3

p1 = a0 + al + a2

p2 = a0 + al + a3

p3 = a0 + a2 + a3

where a0, a1, a2, a3 are the message digits and p0, p1. p2. p3 are parity-check digits. The codewords are in the format (a0, a1, a2. a3, p0, p1. p2, p3).

1. Find all valid codewords for this scheme.

2. Use an example to show how this coding scheme can detect a 3-bit error but not a 4-bit error.

3. Use an example to show how this coding scheme can correct a single-bit error but not a double-bit error.

4. Assuming that parts (2) and (3) are correct in all cases, what is the minimum Hamming distance of this coding scheme?r

Step by Step Solution

★★★★★

3.55 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

1 if p0 0 then a0 a1 a2 a3 0 if p1 0 then a0 a1 a2 0 if p2 0 then a0 a1 a3 0 if p3 0 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Use an example to show how you could use lean thinking with a supplier and a customer.

Use an example to explain how a budget could be used to allocate resources in a university.

What is the minimum Hamming distance?

Consider a portfolio of two stocks whose statistical parameters are given below. Stock A: Annual mean return = 15%, annual standard deviation of return = 30%. Stock B: = 8%, = 15%. Correlation(A,B)...

The following e-mail message has errors in spelling, proofreading, noun plurals, conversational tone, unfamiliar words, and other writing techniques studied in this chapter. You may either (a) Use...

Find the minimum distance of the codes. The code with parity check matrix 1 0 0 P = | 1 1 1 1 1 0 0 1

Find the minimum distance of the codes. The code with parity check matrix P = [I | A], where 1 0 1 1 0 1 0 1 1 1 1 1 1 10 0 Lo

Let C be a linear (n, k, d) code with parity check matrix P. Prove that d = n - k + 1 if and only if every n - k columns of P are linearly independent.

54. Consider the Ehrenfest urn model in which M molecules are distributed between two urns, and at each time point one of the molecules is chosen at random and is then removed from its urn and placed...

Graph the curve whose parametric equations are given and show its orientation Find the rectangular equation of the curve x 2t 5 y t 6 0 t 4 Choose the correct graph below LY The rectangular equation...

Choose a business or a business process and map its inputs, outputs, and operations in an input-transformation-output process.

A double-pipe heat exchanger operating in the parallel-flow mode carries glycerin in the inner pipe and water in the annular region. The glycerin enters the heat exchanger at 90C at a mass flow rate...

8. Your father who is a manager, broke his arm because he slipped and fell in a hotel room shower while on a business trip. Is your father entitled to workers' compensation benefits? 3. A. 5.

Spade Manufacturing produces surfboards. The company uses a normal-costing system and allocates manufacturing overhead on the basis of direct manufacturing labor-hours. Most of the company's...

Telnex Corporation maintains its internal inventory records using first - in , first - out ( FIFO ) under a perpetual inventory system. The following information relates to its inventory during the...

Suppose a local college has tasked you to develop a database that will keep track of students and the courses that they have taken. In addition to tracking the students and courses, the client wants...

Last month when Holiday Creations, Incorporated, sold 40,000 units, its sales, variable expenses, and fixed expenses were $160,000,$132,800, and $39,800, respectively. Required: 1. What is the...

To balance the chemical equation SiH3 + O2 SiO2 + HO, you could introduce coefficients a, b, c, d and write aSiH3 + bO2 cSiO + dHO then write linear equations for each element. The equation for Si...

You are given the representation: Where the equality holds given the sequence of information sets {I t . The underlying process X t is known to follow the SDE: dX t = ?dt + ?dW t Determine the g(-)...

Let the random variable Xn have a binomial distribution: Where each Bi is independent and i distributed according to We can look at X n as the cumulated sum of a series of events that occur over...

Consider a fixed-payer, plain vanilla, interest rate swap paid in arrears with the following characteristics: (1) The start date is in 12 months, the maturity is 24 months. (2) Floating rate is 6...

6. Time refers to your use of chronemic cues to communicate.

5. Space refers to your use of proxemics, including intimate, personal, social, and public space. Example: I will be more aware of others nonverbal messages about space because these messages may...

1.1 Review how communication skills determine leadership qualities