Construction of Polar Codes for Arbitrary Discrete Memoryless Channels

被引:17
|
作者
Gulcu, Talha Cihad [1 ,2 ,3 ]
Ye, Min [1 ]
Barg, Alexander [1 ,2 ,4 ]
机构
[1] Univ Maryland, Dept Elect & Comp Engn, College Pk, MD 20742 USA
[2] Univ Maryland, Inst Syst Res, College Pk, MD 20742 USA
[3] TUBITAK Adv Technol Res Inst, TR-06800 Ankara, Turkey
[4] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127051, Russia
关键词
Channel degrading; greedy symbol merging; polarizing transforms; POLARIZATION; CAPACITY; MATRICES;
D O I
10.1109/TIT.2017.2765663
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for the general case, and analyze an algorithm that is based on successive reduction of the output alphabet size of the subchannels in each recursion step. For this procedure, we estimate the approximation error as O(mu(-1)/(q(-1))), where q is the input alphabet size and mu is the "quantization parameter," i.e., the maximum size of the subchannel output alphabet allowed by the algorithm. The complexity of the code construction scales as O(N-mu(2) log mu), where N is the length of the code. We also show that if the polarizing operation relies on modulo-q addition, it is possible to merge subsets of output symbols without any loss in subchannel capacity. Performing this procedure before each approximation step results in a further speed-up of the code construction, and the resulting codes have smaller gap to capacity. We also show that a similar acceleration can be attained for polar codes over finite field alphabets. Experimentation shows that the suggested construction algorithms can be used to construct long polar codes for alphabets of size q = 16 and more with acceptable loss of the code rate for a variety of polarizing transforms.
引用
收藏
页码:309 / 321
页数:13
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