---
title: "Importance of source encoder; Huffman algorithm"
subject: "Communication Systems"
chapter: 6
key: "semester_6/communication_systems:source-encoder-huffman-algorithm"
source: https://www.bctengineer.com/q/semester_6/communication_systems/source-encoder-huffman-algorithm
site: BCT Engineering
---

# Importance of source encoder; Huffman algorithm

Communication Systems · Chapter 6: Baseband Digital Data Transmission

- Asked in: 2070 Chaitra (CS II), 2+3 marks
- Video: [Huffman Coding (Basics, Algorithm, Procedure & Example) Explained in Digital Communication](https://www.youtube.com/watch?v=HmBH30NrM7c) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/source-encoder-huffman-algorithm
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-6

## Question

Elaborate importance of source encoder? Write algorithm for Huffman's coding.

## Short answer

Source encoder reduces bit rate by assigning shorter codes to frequent symbols, matching average length to entropy. Huffman algorithm: repeatedly merge two lowest-probability symbols, assign bits 0/1, and read codes backwards from final root to leaves.

## Answer

#### Importance of source encoder

The **source encoder** converts the source symbols into binary code words with the minimum average number of bits by removing redundancy.

- It reduces the average code length toward the entropy ($\bar L \to H$), so the bit rate, bandwidth and power needed are reduced.
- It gives short code words to frequent symbols and long ones to rare symbols (variable-length coding).
- It produces uniquely decodable (prefix) codes, so the receiver can decode without separators.
- It saves storage space and makes room for channel coding redundancy.

#### Huffman coding algorithm

1. **Sort:** list all source symbols in decreasing order of probability.
2. **Merge:** combine the two symbols of lowest probability into one new symbol whose probability is the sum of the two.
3. **Reorder:** insert the new probability into the list in its proper place (as high as possible among equal values); the list now has one fewer entry.
4. **Repeat** steps 2–3 until only one entry (probability 1) is left.
5. **Assign bits:** at each merge, give 0 to one branch (upper) and 1 to the other (lower).
6. **Read codes:** trace each symbol's path from the final stage back to its original position; the bits along the path form its code word.
7. **Evaluate:** $\bar L = \sum p_i l_i$, $H = \sum p_i\log_2(1/p_i)$, efficiency $\eta = H/\bar L$.

**Short example:** $P = \{0.5, 0.25, 0.125, 0.125\}$ → merge 0.125 + 0.125 = 0.25, then 0.25 + 0.25 = 0.5, then 0.5 + 0.5 = 1. Codes: 0, 10, 110, 111; $\bar L = 1.75 = H$, $\eta = 100\%$.

## Check yourself

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

1. What is a benefit of the source encoder?
   A. It adds error-correcting redundancy
   B. It reduces average code length toward entropy, saving bandwidth and power
   C. It increases the bit rate
   D. It modulates the carrier
   Answer: B. Removing redundancy lowers bit rate, bandwidth, power and storage. (Key point: Importance of source encoder)

2. At each Huffman step which entries are combined?
   A. The two with highest probability
   B. The two with lowest probability
   C. The first and last
   D. Any two equal ones
   Answer: B. The two lowest probabilities are replaced by their sum. (Key point: Huffman merge step)

3. How is a symbol's code word obtained in Huffman coding?
   A. Bits along its path from the final stage back to its original position
   B. Its binary index
   C. The bits of its probability
   D. Random assignment
   Answer: A. 0/1 labels assigned at each merge are read along the path of the symbol. (Key point: Code reading)

## Related in Communication Systems

- [Source coding aim; Huffman "Kun Mandir Ma Janchhau Yatri"](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahuffman-kun-mandir) — Communication Systems, chapter 6
- [Source vs channel coding; Huffman for five symbols](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asource-channel-huffman-five) — Communication Systems, chapter 6
- [Importance of source coding; Huffman for eight symbols at 1000 symbols/s](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asource-coding-huffman-eight-1000) — Communication Systems, chapter 6
- [Source coding; Huffman for five symbols (0.3, 0.25, 0.2, 0.15, 0.1)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asource-coding-huffman-five-s0) — Communication Systems, chapter 6
- [Huffman and Shannon-Fano coding of A0–A4](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahuffman-sf-a0-a4-compare) — Communication Systems, chapter 6
- [Types of noise; Shannon-Fano and Huffman coding efficiency](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anoise-types-shannon-fano-huffman) — Communication Systems, chapter 6

## Related in other subjects

- [Source coding; fixed vs variable length codes](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Asource-coding-fixed-variable) — Data Communication, chapter 8
- [Huffman coding principle](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ahuffman-principle) — Data Communication, chapter 8, asked 3×
- [Huffman coding of a sentence (Khoji Rahechha)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ahuffman-khoji-rahechha) — Data Communication, chapter 8
- [Algorithm for Huffman code](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Ahuffman-code-algorithm) — Data Structure and Algorithm, chapter 6