Principles of Communication Engineering

Answer

Correct Option: (ii) Decoding convolutional codes

Explanation

Viterbi algorithm is maximum-likelihood trellis decoder for convolutional codes (and trellis-coded modulation). Uses dynamic programming over trellis states to find most likely path.

Not for cyclic code encoding (LFSR), filtering, or pure error detection.

Final Answer

Decoding convolutional codes → Option (ii).

Answer

Correct Option: (ii) Generator polynomial

Explanation

Cyclic codes $(n,k)$ are ideals in $\mathbb{F}_2[x]/(x^n-1)$, generated by $g(x)$ dividing $x^n-1$. Codewords $c(x)=m(x)g(x)$. Generator $g(x)$ degree $n-k$, parity check $h(x)=(x^n-1)/g(x)$. Example Hamming (7,4) $g(x)=x^3+x+1$.

Not frequency response, trellis, Fourier.

Final Answer

Generator polynomial → Option (ii).

Answer

Correct Option: (ii) Parity checking and syndrome

Explanation

Block coding $(n,k)$: $r=n-k$ parity bits, generator $G$, parity $H$, syndrome $s=yH^T$. Error detection via syndrome non-zero. Not modulation index, quantization noise, clock sync.

Final Answer

Parity/syndrome → Option (ii).

Answer

Correct Option: (iii) $3$

Explanation

Single-bit correction: $t=1$ → Hamming distance $d_{min}\ge2t+1=3$. Detect $t$ errors needs $d\ge t+1$.

Final Answer

$3$ → Option (iii).

Answer

CRC: Polynomial division $r(x)=m(x)x^r \bmod g(x)$, transmit $m||r$. Generation LFSR taps $g(x)=x^3+x+1$ CRC-3. Detection divide $y(x)/g(x)$ remainder 0 OK else error. Detects burst ≤$r$ bits. Uses Ethernet, HDLC, disk. Overhead $r$ bits per $k$ data.

Answer

Hamming (7,4): Parity bits at 1,2,4. Received 1011010, even parity checks: $p_1=1\oplus1\oplus0\oplus0=0$, $p_2=0\oplus1\oplus1\oplus0=0$, $p_4=1\oplus0\oplus1\oplus0=0$ syndrome 000 → no error. Data bits 3,5,6,7 =1010. If odd parity syndrome 111 → position 7 error. Method: syndrome binary = error position, flip.

Answer

Huffman: Variable-length prefix optimal. Merge two smallest probabilities iteratively, assign 0/1. Example 0.4,0.3,0.2,0.1→ codes 0,10,110,111 average 1.9 bits near entropy 1.84. ZIP, JPEG. Prefix-free uniquely decodable.

Answer

Need for error control: Channel noise causes bit errors → unreliable. Techniques: Detection (parity, CRC) + ARQ, Correction (FEC Hamming, convolutional, Turbo) with $t=\lfloor(d_{min}-1)/2\rfloor$. Ensures reliability.

Answer

Shannon-Fano top-down split near equal sum, not always optimal. Huffman bottom-up merging smallest, optimal. Huffman minimal expected length $L=\sum p_i l_i$, efficiency $\eta=H/L$ higher. Both prefix-free.