---
title: "ISI; modified duobinary for 10110011"
subject: "Communication Systems"
chapter: 6
key: "semester_6/communication_systems:isi-modified-duobinary-10110011"
source: https://www.bctengineer.com/q/semester_6/communication_systems/isi-modified-duobinary-10110011
site: BCT Engineering
---

# ISI; modified duobinary for 10110011

Communication Systems · Chapter 6: Baseband Digital Data Transmission

- Asked in: 2075 Chaitra (CS II), 6+4 marks
- Video: [Modified Duobinary Encoder with Precode||Digital Communication||Wireless COmmunication](https://www.youtube.com/watch?v=DHER2NLk-JI) — Engineering Basics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/isi-modified-duobinary-10110011
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-6

## Question

What do you understand by Inter Symbol Interference (ISI)? Explain modified Duobinary coding technique and illustrate it using binary input sequence 10110011.

## Short answer

ISI is overlapping of pulses causing errors. Modified duobinary uses c_k = a_k - a_{k-2} with three levels; no DC. For input 10110011, precoded output yields c_k: +2,0,-2,+2,0,0,+2,-2, decoded to 10110011.

## Answer

#### Inter Symbol Interference (ISI)

**ISI** is the overlapping of neighbouring pulses in a digital signal, so that at the sampling instant of one symbol the received value also contains the tails of other symbols. It appears because a band-limited channel spreads each pulse in time (a pulse limited in bandwidth cannot be limited in time).

The receiver output at the sampling instant $t_i = iT_b$ is

$$
y(t_i) = \mu a_i + \mu\sum_{k\ne i} a_k\,p\big((i-k)T_b\big) + n(t_i)
$$

The first term is the wanted symbol, the second is ISI, the third is noise.

**Causes:** limited channel bandwidth, non-ideal filters, multipath and dispersion in cables or fibres, timing errors at the receiver.

**Effects:** wrong decisions even without noise; higher bit error rate; reduced eye opening and noise margin; sensitivity to timing jitter.

```text
 pulse k-1     pulse k     pulse k+1
     /\         /\          /\
 ___/  \_     _/  \_      _/  \___
         \___/      \____/
        tail of k-1 adds to k
```

**Remedies:** Nyquist pulse shaping (raised cosine), correlative coding (duobinary, modified duobinary), and equalization.

#### Modified duobinary coding

Modified duobinary introduces a controlled ISI between a symbol and the one two bit intervals before it:

$$
c_k = a_k - a_{k-2}, \qquad H(f) = 2j\sin(2\pi fT_b)\,e^{-j2\pi fT_b},\ |f| \le \frac{1}{2T_b}
$$

$H(0) = 0$, so the spectrum has **no DC component**. The output takes three levels (−2, 0, +2). A precoder $d_k = b_k \oplus d_{k-2}$ is used so that each bit is decoded from one sample: $|c_k| = 2 \Rightarrow 1$, $c_k = 0 \Rightarrow 0$.

#### Illustration for 10110011

Assume $d_{-1} = d_0 = 0$; level mapping $d = 1 \to +1$, $d = 0 \to -1$.

| k | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| $b_k$ | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| $d_{k-2}$ | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| $d_k$ | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
| $a_k$ | +1 | −1 | −1 | +1 | −1 | +1 | +1 | −1 |
| $a_{k-2}$ | −1 | −1 | +1 | −1 | −1 | +1 | −1 | +1 |
| $c_k$ | +2 | 0 | −2 | +2 | 0 | 0 | +2 | −2 |
| $\hat b_k$ | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |

The decoded output **10110011** matches the input.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is intersymbol interference?
   A. Noise added by the receiver
   B. Overlap of neighbouring pulses so a sample contains tails of other symbols
   C. Loss of signal power
   D. Interference from other channels
   Answer: B. A band-limited channel spreads pulses, so tails of other symbols add to the wanted sample. (Key point: Meaning of ISI)

2. Which is an effect of ISI?
   A. Wrong decisions even without noise
   B. Lower bit error rate
   C. Wider eye opening
   D. Less sensitivity to jitter
   Answer: A. ISI reduces the eye opening and noise margin, raising bit error rate. (Key point: Effects of ISI)

3. The modified duobinary output c_k = a_k - a_(k-2) takes which levels?
   A. -1, +1
   B. 0, +1
   C. -2, 0, +2
   D. -3 to +3
   Answer: C. With a = +-1 the difference can be -2, 0 or +2. (Key point: Modified duobinary levels)

4. With precoding, if c_k = 0 the decoded bit is:
   A. 1
   B. 0
   C. Same as the previous bit
   D. Undefined
   Answer: B. |c_k| = 2 means b = 1, and c_k = 0 means b = 0. (Key point: Decoding with precoder)

## Related in Communication Systems

- [Reducing ISI; modified duobinary with precoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-reduce-modified-duobinary) — Communication Systems, chapter 6
- [ISI; duobinary with precoder for 0010110](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-duobinary-precoder-0010110) — Communication Systems, chapter 6
- [ISI; Nyquist criteria; duobinary with example](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-nyquist-duobinary-example) — Communication Systems, chapter 6, asked 2×
- [Correlative coding; minimizing error in duobinary](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acorrelative-coding-duobinary-error) — Communication Systems, chapter 6
- [ISI; solutions for zero ISI; duobinary with precoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-zero-isi-duobinary-precoder) — Communication Systems, chapter 6
- [Nyquist criteria for zero ISI; duobinary difficulties](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anyquist-zero-isi-duobinary-difficulties) — Communication Systems, chapter 6

## Related in other subjects

- [Line coding in PCM and the right technique](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aline-coding-pcm-solution) — Telecommunications, chapter 3