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Polar code construction method for implementing code word optimal distribution under memory channel by utilizing Homophonic encoding

A construction method and optimal distribution technology, applied in the field of communication channel coding, can solve the problem that the memory channel is not optimal

Inactive Publication Date: 2017-06-13
BEIHANG UNIV
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  • Claims
  • Application Information

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Problems solved by technology

Usually, the input of the traditional polar code is a uniform distribution of i.i.d (independent and identical distribution), which is not optimal in the memory channel

Method used

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  • Polar code construction method for implementing code word optimal distribution under memory channel by utilizing Homophonic encoding
  • Polar code construction method for implementing code word optimal distribution under memory channel by utilizing Homophonic encoding
  • Polar code construction method for implementing code word optimal distribution under memory channel by utilizing Homophonic encoding

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Embodiment

[0052] Example : The block length l=2 of the information sequence, the polar code codeword construction embodiment of the frame length N=8 of the input sequence.

[0053] In this example, the information input block length l=2 of Homophonic encoding, the tth group information sequence The frozen set length of the polar code|I c |=4, information bit length |I|=4. Obtaining Frozen Set I by Monte Carlo Method c = {1, 3, 5, 6} and information set I = {2, 4, 7, 8}. Under the memory channel, the channel in this embodiment has two states, denoted as s={0,1}, and the initial state is set to S 0 =0, the optimal distribution of output codewords is:

[0054] (p x,s′|s″ (0,0|0),p x,s′|s″ (0,0|1),p x,s′|s″ (1,1|0),p x,s′|s″ (1,1|1))=(p 1 ,p 2 ,p 3 ,p 4 )

[0055] and 0≤p 1 ,p 2 ,p 3 ,p 4 ≤1,p 1 +p 2 +p 3 +p 4 =1, here, x is the input information bit, s' represents the next state of the channel, and s "represents the current state of the channel. Here, the codeword x...

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Abstract

The invention provides a polar code construction method for implementing code word optimal distribution under a memory channel by utilizing Homophonic encoding. In the method, an input information sequence meets independent uniform distribution; firstly, distribution characteristics of the input information sequence are changed by the Homophonic encoding, so that the input information sequence obeys specific probability distribution under the corresponding memory channel, which can implement channel capacity; and then the sequence which obeys the specific probability distribution is used as an input sequence of polar encoding so as to carry out polar encoding and generate encoded code words. The code words obey the optimal probability distribution under the corresponding memory channel so as to achieve an effect that under the memory channel, the polar encoding method can reach channel capacity. According to the polar code construction method provided by the invention, pre-encoding is carried out by Homophonic codes to implement optimal distribution of the polar encoded output code words, an original polar encoding structure is kept, and reachability of channel capacity under the memory channel is implemented.

Description

technical field [0001] The invention belongs to the technical field of communication channel coding, and specifically refers to a polar code construction method for realizing optimal distribution of code words by using Homophonic coding under a memory channel. Background technique [0002] Polar Codes, that is, polar codes, was developed by E. A new type of channel coding is proposed. Polar codes are designed based on channel polarization (Channel Polarization), which is the first constructive coding scheme that can prove channel capacity through rigorous mathematical methods. Polar code has regular structural rules, low encoding and decoding complexity, and is easy to jointly design and optimize with other communication technologies. These advantages make Polar codes have good application prospects. However, most of the current research on Polar codes is to achieve capacity in memoryless channels. In actual communication systems, due to the complexity of the communicati...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L1/00H03M13/13
CPCH04L1/0057H03M13/13H04L1/0056H04L1/0064
Inventor 刘荣科冯宝平王闰昕赵岭
Owner BEIHANG UNIV
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