--- title: "Interleaving and MLSE" subject: "Wireless Communication" chapter: 5 key: "semester_7/wireless_communication:interleaving-mlse" source: https://www.bctengineer.com/q/semester_7/wireless_communication/interleaving-mlse site: BCT Engineering --- # Interleaving and MLSE Wireless Communication · Chapter 5: Equalization and Diversity - Asked in: 2081 Bhadra, 4+4 marks - Video: [GEL7114 Module 4.1 Maximum Likelihood Sequence Estimation (MLSE)](https://www.youtube.com/watch?v=tL8lTuQR3dY) — Leslie Rusch - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/interleaving-mlse - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-5 ## Question Elaborate the working principle behind interleaving with an appropriate diagram. Explain the working of Maximum Likelihood Sequence Estimation (MLSE). ## Short answer Interleaving spreads burst errors by writing coded bits row-wise and reading column-wise, so a fade affects only one bit per code word. MLSE treats the ISI channel as a finite-state machine and uses the Viterbi algorithm to find the sequence with minimum squared error, providing optimal equalization at the cost of exponential complexity. ## Answer #### Interleaving **Interleaving** rearranges the order of coded bits before transmission so that a burst of errors caused by a deep fade is spread out into isolated single errors after de-interleaving. Error-correcting codes can correct scattered errors easily but fail on long bursts, so interleaving gives **time diversity** without adding redundancy. **Block interleaver (m rows × n columns):** bits are written into the array **row by row** and read out **column by column**. The receiver de-interleaver does the reverse. ```text Write by rows → Read by columns ↓ 1 2 3 4 out: 1 5 9 13 2 6 10 14 5 6 7 8 3 7 11 15 4 8 12 16 9 10 11 12 13 14 15 16 ``` Suppose a fade wipes out 4 consecutive transmitted bits, e.g. 1, 5, 9, 13. After de-interleaving they appear in different rows (code words), each with only one error, which the decoder can correct. ```text Channel burst: [1 5 9 13] (4 bits in a row) After de-interleave: X 2 3 4 X 6 7 8 one error per code word X 10 11 12 X 14 15 16 ``` The interleaving depth must exceed the burst length, but larger depth adds delay; speech systems therefore limit delay to around 40 ms (GSM interleaves over 8 bursts). #### Maximum Likelihood Sequence Estimation (MLSE) **MLSE** is a non-linear equalizer that, instead of deciding symbols one by one, chooses the **whole data sequence** that is most likely to have produced the received signal. It treats the ISI channel as a finite-state machine and uses the **Viterbi algorithm** to search efficiently. ```text r(t)->[Matched ]->[ MLSE (Viterbi) ]-> data [ filter ] ^ | | +->[Channel estimator] (from training) ``` 1. A training sequence lets the **channel estimator** find the channel impulse response, which spans the current symbol plus L earlier symbols (channel memory L). 2. The trellis then has M^L states (M = alphabet size). For each received sample the Viterbi algorithm computes path metrics (squared distance between the received sample and the expected noise-free output) for every state transition. 3. Only the best ("survivor") path into each state is kept. 4. After enough samples the survivor with the minimum total metric gives the most likely transmitted sequence. MLSE is optimal in the sense of minimizing sequence error probability and handles severe ISI, but complexity grows exponentially with channel length. GSM uses a Viterbi (MLSE) equalizer covering about 4 bit periods (≈ 15 µs) of delay spread. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does interleaving do to a burst of errors caused by a deep fade? A. It removes them by adding extra parity bits B. It spreads them into isolated single errors after de-interleaving C. It lowers the transmit power needed during the fade D. It converts them into longer bursts the code can detect Answer: B. After de-interleaving the burst bits fall into different code words, so each has few errors that the decoder can correct. (Key point: Purpose of interleaving) 2. In a 4x4 block interleaver, a fade wipes out 4 consecutive transmitted bits (1, 5, 9, 13). What happens after de-interleaving? A. One code word has all 4 errors B. Each code word (row) has just one error C. All four errors vanish automatically D. Two code words have two errors each Answer: B. The four bits belong to four different rows, so each code word has one correctable error. (Key point: Effect of 4-bit burst) 3. In the Viterbi search used by MLSE, what is kept at each state? A. All paths entering it B. The longest path into it C. Only the best (minimum-metric) survivor path into it D. The path with the maximum metric Answer: C. Only the survivor with the smallest squared-distance metric into each state is retained, keeping the search efficient. (Key point: Viterbi survivor path) 4. A channel of L taps with alphabet size M has how many states in MLSE, and what is the consequence? A. L^M states; complexity is constant B. M*L states; complexity is linear in M C. 2 states always; complexity is negligible D. M^L states; complexity grows exponentially with channel length Answer: D. The trellis has M^L states, so complexity grows exponentially with channel memory. (Key point: MLSE complexity) ## Related in Wireless Communication - [MLSE and time diversity](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amlse-time-diversity) — Wireless Communication, chapter 5 - [MLSE equalization](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amlse-equalization) — Wireless Communication, chapter 5 - [Need for interleaving](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ainterleaving-need) — Wireless Communication, chapter 5 - [Direct sequence spread spectrum (DSSS)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adsss-block-diagram) — Wireless Communication, chapter 4 ## Related in other subjects - [Working principle of dc generator with diagram](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Adc-generator-principle-diagram) — Electrical Machines, chapter 3 - [DM techniques; likelihood and distance principle](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adm-techniques-close-data-alike) — Data Mining, chapter 3 - [Working principle of a digital telephone exchange](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-telephone-exchange-principle) — Telecommunications, chapter 4, asked 4× - [Combined cycle advantages and working principle](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Acombined-advantages-working) — Power Plant Equipment, chapter 8, asked 2×