Suggest edit — SU-ENGR76 MAY282024

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title: "SU-ENGR76 MAY282024"
source: https://www.jemoka.com/posts/kbhsu_engr76_may282024/
date: 2024-05-28
---

Convolutional Code The output sequences of Convolutional Code behaves like a five bit difference in Hamming Distance.
Decoding brute force decoding: precompute, for a sequence length of \(k\), compute \(2^{k}\) sequneces and what they should correspond to in our target code &mdash; of course, this is not computationally feasible Virtirbi Algorithm: time complexity &mdash; \(4(k+2)\), \(8(k+2)\) 4 possible blocks of 2, and 8 comparisons for Hamming Distance: in general \(k_0\) in general \(k_0\) of source symbols entering the decoder \(n_0\) of symbols produced by decoder at each step constrain length \(m_0\), how many bits are considered for the Convolutional Code setup we discussed, we have \(k_0=1\), \(n_0=2\), and \(m_0 = 3\) (one bit produces 2 bits, and we consider 3 bits per step.)
Comparison of Codes Code Rate M L dmin repetition code 1/3 2 3 3 Hamming Code 4/7 16 7 3 Convolutional Code 1/2 ≈ 5 Bit Error Rate KEY GOAL: if I hand you an error rate of the uncoded transmission, what would be the bit error rate of a given resulting error-correction code?