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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Sequential decoding ： ウィキペディア英語版 Sequential decoding Sequential decoding is a limited memory technique for decoding tree codes. Sequential decoding is mainly used is as an approximate decoding algorithm for long constraint-length convolutional codes. This approach may not be as accurate as the Viterbi algorithm but can save a substantial amount of computer memory. Sequential decoding explores the tree code in such a way to try to minimise the computational cost and memory requirements to store the tree. There is a range of sequential decoding approaches based on choice of metric and algorithm. Metrics include: *Fano metric *Zigangirov metric *Gallager metric Algorithms include: *Stack algorithm *Fano algorithm *Creeper algorithm ==Fano metric== Given a partially explored tree (represented by a set of nodes which are limit of exploration), we would like to know the best node from which to explore further. The Fano metric (named after Robert Fano) allows one to calculate from which is the best node to explore further. This metric is optimal given no other constraints (e.g. memory). For a binary symmetric channel (with error probability $p$) the Fano metric can be derived via Bayes theorem. We are interested in following the most likely path $P\_i$ given an explored state of the tree $X$ and a received sequence $$. Using the language of probability and Bayes theorem we want to choose the maximum over $i$ of: :$\backslash Pr(P\_i|X,)\; \backslash propto\; \backslash Pr(|P\_i,X)\backslash Pr(P\_i|X)$ We now introduce the following notation: *$N$ to represent the maximum length of transmission in branches *$b$ to represent the number of bits on a branch of the code (the denominator of the code rate, $R$). *$d\_i$ to represent the number of bit errors on path $P\_i$ (the Hamming distance between the branch labels and the received sequence) *$n\_i$ to be the length of $P\_i$ in branches. We express the likelihood $\backslash Pr(|P\_i,X)$ as $p^\; (1-p)^\; 2^$ (by using the binary symmetric channel likelihood for the first $n\_ib$ bits followed by a uniform prior over the remaining bits). We express the prior $\backslash Pr(P\_i|X)$ in terms of the number of branch choices one has made, $n\_i$, and the number of branches from each node, $2^$. Therefore: :$$ \begin \Pr(P_i|X,) &\propto p^ (1-p)^ 2^ 2^ \\ &\propto p^ (1-p)^ 2^ 2^ \end We can equivalently maximise the log of this probability, i.e. :$$ \begin &d_i \log_2 p + (n_ib-d_i) \log_2 (1-p) +n_ib-n_iRb \\= &d_i(\log_2 p +1-R) + (n_ib-d_i)(\log_2 (1-p) + 1-R) \end This last expression is the Fano metric. The important point to see is that we have two terms here: one based on the number of wrong bits and one based on the number of right bits. We can therefore update the Fano metric simply by adding $\backslash log\_2\; p\; +1-R$ for each non-matching bit and $\backslash log\_2\; (1-p)\; +\; 1-R$ for each matching bit. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sequential decoding」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.