Polar Coding for Non-Stationary Channels
Polar Coding for Non-Stationary Channels
复制标题
非平稳信道下的极化编码
DOI：
10.1109/tit.2020.3020929
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发表时间：
2016-11
影响因子：
2.5
通讯作者：
Hessam Mahdavifar
中科院分区：
文献类型：
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作者：
Hessam Mahdavifar
独立二进制输入无内存对称（bms）的任意序列的极性编码$ \ left \ {{w_ {i}} \ right \} _ {i = 1}^{n} $一系列通道被称为非平稳的通道序列，并在数据符号经历不同和独立的通道特征的应用中被认为是发射器和接收器完全知道的（相干方案） ）。 $。目标是以$ r $ $ $ $ w_ {i} $的对称能力的平均值，由$ \ overline {i} _ {n} $表示。使用Arıkan的通道极化转换构建极地编码方案，并在每个极化水平上尤其是某些跳过的操作。 } _ {i = 1}^{n} $和$ p_ {e} $，其中$ 0，我们构造了一个长度$ n $的极性代码和速率$ r $保证最多$ p_ {e的块错误概率} $用于通过$ \ left \ {{w_ {i}} \ right \} _ {i = 1}^{n} $的变速箱$ _ {n} - r）^{\ mu}} $，其中$ \ mu $是常数，$ \ kappa $是一个常数，具体取决于$ p_ {e} $和$ \ mu $。 $ \ mu $上的上限是：$ \ mu \ leqslant 7.34 $用于非平稳二进制擦除通道和$ \ mu \ mu \ leqslant 8.54 $，用于一般的非平稳BMS通道。保留$ o（n \ log n）$在渐近的意义上的Arıkan的复杂性。 _ {i = 1}^{\ infty} $，我们提出的方案实现了平均对称能力$ \ overline {i}（\ left \ w_ {w_ {w_ {i}}} \ right \} \ infty}）\，\，{\ textstyle \ stackrel {\ mathrm {def}}} {=}}}}}} \，\，\，\ lim _ { i = 1}^{n} i（w_ {i}）$，假设存在限制。
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left \{{W_{i}}\right \}_{i=1}^{N}$ is considered. Such a sequence of channels is referred to as a non-stationary sequence of channels and arises in applications where data symbols experience different and independent channel characteristics. The sequence of channels is assumed to be completely known to both the transmitter and the receiver (a coherent scenario). Also, at each code block transmission, each of the channels is used only once. In other words, a codeword of length $N$ is constructed and then the $i$ -th encoded bit is transmitted over $W_{i}$ . The goal is to operate at a rate $R$ close to the average of the symmetric capacities of $W_{i}$ ’s, denoted by $\overline {I}_{N}$ . To this end, we construct a polar coding scheme using Arıkan’s channel polarization transform in combination with certain permutations at each polarization level and certain skipped operations. In particular, given a non-stationary sequence of BMS channels $\left \{{W_{i}}\right \}_{i=1}^{N}$ and $P_{e}$ , where $0 , we construct a polar code of length $N$ and rate $R$ guaranteeing a block error probability of at most $P_{e}$ for transmission over $\left \{{W_{i}}\right \}_{i=1}^{N}$ such that $N \leqslant \frac {\kappa }{(\overline {I}_{N}- R)^{\mu }}$ , where $\mu $ is a constant and $\kappa $ is a constant depending on $P_{e}$ and $\mu $ . We further show a numerical upper bound on $\mu $ that is: $\mu \leqslant 7.34$ for non-stationary binary erasure channels and $\mu \leqslant 8.54$ for general non-stationary BMS channels. The encoding and decoding complexities of the constructed polar code preserve $O(N \log N)$ complexity of Arıkan’s polar codes. In an asymptotic sense, when coded bits are transmitted over a non-stationary sequence of BMS channels $\left \{{W_{i}}\right \}_{i=1}^{\infty }$ , our proposed scheme achieves the average symmetric capacity $\overline {I}(\left \{{W_{i}}\right \}_{i=1}^{\infty }) \,\,{\textstyle \stackrel {\mathrm{ def}}{=}}\,\,\lim _{N\rightarrow \infty } \frac {1}{N}\sum _{i=1}^{N} I(W_{i})$ , assuming that the limit exists.