---
title: "Short note: Turbo coding"
subject: "Wireless Communication"
chapter: 6
key: "semester_7/wireless_communication:turbo-coding-note"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/turbo-coding-note
site: BCT Engineering
---

# Short note: Turbo coding

Wireless Communication · Chapter 6: Speech and Channel Coding

- Asked in: 2074 Magh, 5 marks
- Video: [L 22 | Turbo Code Introduction | Information Theory & Coding | Digital Communication |Vaishali Kikan](https://www.youtube.com/watch?v=seirAFhAVas) — Dopamine
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/turbo-coding-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-6

## Question

Write a short note on turbo coding.

## Short answer

Turbo coding concatenates two recursive systematic convolutional encoders separated by an interleaver, with iterative soft decoding, approaching Shannon limit within 0.5–1 dB. The decoder exchanges extrinsic information between SISO stages. Used in 3G, LTE and deep-space links.

## Answer

**Turbo coding** is a forward error-correction (FEC) technique, introduced by Berrou, Glavieux and Thitimajshima in 1993, that uses **parallel concatenated recursive systematic convolutional (RSC) codes** joined by an **interleaver**, with **iterative soft decoding**. It comes within about 0.5–1 dB of the Shannon limit.

**Encoder**

```text
 d(k) --+------------------------------> x (systematic)
        +-->[RSC encoder 1]------------> y1 (parity 1)
        +-->[interleaver]->[RSC enc. 2]-> y2 (parity 2)
                 |
        [puncturing / MUX] -> rate 1/3 (or 1/2)
```

- The data bits are sent unchanged (systematic part).
- Encoder 1 produces parity from the data in natural order; encoder 2 produces parity from an interleaved (permuted) copy.
- The interleaver makes the two parity streams nearly independent, so a pattern that is weak for one encoder is strong for the other.
- Puncturing can raise the code rate from 1/3 to 1/2.

**Decoder**

```text
     +--------------------------------------+
     v                                      |
 x,y1->[SISO decoder 1]->[interleave]->[SISO decoder 2]
                                  y2-->^        |
           extrinsic info  <-[de-interleave]<---+
                                   after N iterations
                                   -> hard decision
```

- Two soft-input soft-output decoders (MAP/BCJR or SOVA) exchange **extrinsic information** (log-likelihood ratios).
- Each iteration improves the reliability of the bit estimates; 4–8 iterations are typical.

**Merits:** near-Shannon-limit performance at low SNR. **Demerits:** decoding delay and complexity, and an "error floor" at very low BER. Used in 3G (WCDMA, CDMA2000), LTE data channels and deep-space links.

## Check yourself

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

1. A turbo encoder is built from which components?
   A. Two parallel recursive systematic convolutional encoders joined by an interleaver
   B. Two cascaded block encoders with no interleaver
   C. A single non-recursive convolutional encoder with puncturing
   D. A Reed-Solomon encoder followed by a Viterbi encoder
   Answer: A. Turbo codes use parallel concatenated RSC encoders, with an interleaver feeding the second one. (Key point: Turbo encoder structure)

2. Why is an interleaver placed before the second RSC encoder?
   A. To raise the code rate to 1/2
   B. To make the two parity streams nearly independent so a pattern weak for one encoder is strong for the other
   C. To remove the systematic bits
   D. To speed up the decoding by skipping iterations
   Answer: B. The permuted copy gives decorrelated parity, so error patterns that fool one encoder are caught by the other. (Key point: Role of interleaver)

3. What do the two SISO decoders exchange in each iteration?
   A. Hard-decision bits
   B. Raw channel samples only
   C. Extrinsic information as log-likelihood ratios
   D. Puncturing patterns
   Answer: C. Decoders pass extrinsic LLRs to each other, improving bit reliability with each iteration. (Key point: Iterative soft decoding)

4. Which pair correctly gives a merit and a demerit of turbo coding?
   A. Low complexity; error floor at high SNR
   B. Near-Shannon performance at low SNR; decoding delay and error floor at very low BER
   C. Zero delay; poor performance at low SNR
   D. No interleaver needed; high bit rate only
   Answer: B. Turbo codes get within 0.5-1 dB of the Shannon limit but suffer delay, complexity and an error floor. (Key point: Merits and demerits)

## Related in Wireless Communication

- [Turbo coding and 8×8 Hadamard code](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aturbo-coding-hadamard) — Wireless Communication, chapter 6