Repetition code, cont For Pe<1/2, plerror) is decreasing in n for any e, 3 n large enough so that p(error)<e Code Rate: ratio of data bits to transmitted bits For the repetition codeR= 1/n To send one data bit. must transmit n channel bits "bandwidth expansion In general, an(n, k code uses n channel bits to transmit k data bits Code rate rek/n Goal: for a desired error probability, E, find the highest rate code that can achieve p(error) <eEytan Modiano Slide 4 Repetition code, cont. • For P e < 1/2, P(error) is decreasing in n – ⇒ for any ε, ∃ n large enough so that P (error) < ε Code Rate: ratio of data bits to transmitted bits – For the repetition code R = 1/n – To send one data bit, must transmit n channel bits “bandwidth expansion” • In general, an (n,k) code uses n channel bits to transmit k data bits – Code rate R = k / n • Goal: for a desired error probability, ε, find the highest rate code that can achieve p(error) < ε