基于分段鑿孔的極化碼級(jí)聯(lián)方案
doi: 10.11999/JEIT171113
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1.
重慶理工大學(xué)電氣與電子工程學(xué)院 ??重慶 ??400054
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2.
電子科技大學(xué)物理電子學(xué)院 ??成都 ??611731
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61205106)，中國(guó)博士后科學(xué)基金(2014M552329)，重慶市教委科學(xué)技術(shù)研究項(xiàng)目(KJ1500934, KJ120827)，重慶市科委社會(huì)事業(yè)與民生保障科技創(chuàng)新專項(xiàng)(cstc2017shmsA40019)
Concatenated Polar Codes Scheme Based on Segmented Puncturing
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1.
School of Electrical and Electronic Engineering, Chongqing University of Technology, Chongqing 400054, China
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2.
School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 611731, China
Funds: The National Natural Science Foundation of China (61205106), China Postdoctoral Science Foundation (2014M552329), The Science and Technology Project Affiliated to the Education Department of Chongqing Municipality (KJ1500934, KJ120827), Chongqing Municipal Science and Technology Commission’s Special Project (cstc2017shmsA40019)
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摘要: 極化碼擁有出色的糾錯(cuò)性能，但編碼方式?jīng)Q定了其碼長(zhǎng)不夠靈活，需要通過(guò)鑿孔構(gòu)造碼長(zhǎng)可變的極化碼。該文引入矩陣極化率來(lái)衡量鑿孔對(duì)極化碼性能的影響，選擇矩陣極化率最大的碼字作為最佳鑿孔模式。對(duì)極化碼的碼字進(jìn)行分段，有效減小了最佳鑿孔模式的搜索運(yùn)算量。由于各分段的第1個(gè)碼字都會(huì)被鑿除，且串行抵消譯碼過(guò)程中主要發(fā)生1位錯(cuò)，因此在各段段首級(jí)聯(lián)奇偶校驗(yàn)碼作為譯碼提前終止標(biāo)志，檢測(cè)前段碼字的譯碼錯(cuò)誤并進(jìn)行重新譯碼。對(duì)所提方法在串行抵消譯碼下的性能進(jìn)行仿真分析，結(jié)果表明，相比傳統(tǒng)鑿孔方法，所提方法在10–3誤碼率時(shí)能獲得約0.7 dB的編碼增益，有效提升了鑿孔極化碼的譯碼性能。
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關(guān)鍵詞:
- 極化碼 /
- 串行抵消譯碼 /
- 鑿孔 /
- 奇偶校驗(yàn)碼 /
- 誤碼率
Abstract: Polar codes have outstanding error correction performance, but the code length of conventional polar codes is not compatible because of their coding method. To construct rate-compatible polar codes, a segmented puncturing method is proposed. Using the rate of polarization, the puncturing effect is measured and the codeword is removed to make the largest rate of polarization, which is the optimal puncturing mode. As the first codeword of the optimal puncturing mode is 0, the parity check codes are introduced to detect the decoding error of preceding segments codeword. The decoding performance of the method is simulated, results show that this method can obtain about 0.7 dB coding gain at 10–3 bit error rate compared with the traditional puncturing method, which can effectively improve the performance of the punctured polar codes.-
Key words:
- Polar codes /
- Successive cancellation decoding /
- Puncturing /
- Parity check codes /
- Bit error rate
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表 1 不同分段碼長(zhǎng)s 的譯碼性能增益比較
碼長(zhǎng)N Eb/N0(dB) 32 64 128 256 512 1024 s=4 0 0 0 0 0 0 s=8 0.012 0.036 0.091 0.108 0.138 0.159 s=16 –0.107 –0.043 0.055 0.118 0.188 0.233 最優(yōu)s 8 8 8 16 16 16 對(duì)應(yīng)m 4 8 16 16 32 64 
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表 2 剩余碼長(zhǎng)分配方法
算法1：剩余碼長(zhǎng)分配方法 輸入：N, L,m, s 輸出： ${L_1}$, ${L_2}$, ${n_1}$, ${n_2}$ (1) 定義 ${L_1},\;{L_2}$為各分段中較短與較長(zhǎng)的分段剩余碼長(zhǎng)； (2) 定義 ${n_{\min }},\;{n_{\max }}$為分段剩余碼長(zhǎng)為 ${L_1},\;{L_2}$的分段個(gè)數(shù)； (3) 較短分段剩余碼長(zhǎng) ${L_1} \!=\!\! \left\lfloor \!{\displaystyle\frac{{sL}}{N}}\! \right\rfloor $，較長(zhǎng)分段剩余碼長(zhǎng) ${L_2} \! =\! \! \left\lceil \!{\displaystyle\frac{{sL}}{N}}\! \right\rceil $； (4) ${n_1}$與 ${n_2}$的比值為： $\frac{{{n_1}}}{{{n_2}}} = \frac{{m{L_2} - L}}{{L - m{L_1}}}$； (5) ${L_1}$的個(gè)數(shù) ${n_1} = \frac{{m{L_2}{\rm{ - }}L}}{{{L_2} - {L_1}}}$, ${L_{\max }}$的個(gè)數(shù) ${n_2} = \frac{{L{\rm{ - }}m{L_1}}}{{{L_2} - {L_1}}}$。
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表 3 N=8對(duì)應(yīng)的最佳鑿孔模式
L ${{E} _{\max }}{\rm{(}}{{G}})$ ${{{P}}_{8,L}}$ 7 0.6008 01111111 6 0.6022 01111110 5 0.5949 00011111
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表 4 N=16對(duì)應(yīng)的最佳鑿孔模式
L ${{E} _{\max }}{\rm{(}}{{G}})$ ${{{P}}\!_{16,L}}$ 15 0.5445 0111111111111111 14 0.5635 0111111111111110 13 0.5616 0111111111111100 12 0.5654 0111111111111000 11 0.5764 0111111011111000 10 0.5794 0111111011101000 9 0.5582 0111011011101000
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表 5 PPCA-SC復(fù)雜度比較
信噪比(dB) 時(shí)間復(fù)雜度 1.5(PPCA-SC) 12275 2.0(PPCA-SC) 10858 2.5(PPCA-SC) 10360 SC 10240
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表 6 PPCA-SC平均重復(fù)譯碼次數(shù)比較
碼長(zhǎng) 平均重復(fù)譯碼次數(shù) 256 0.72 512 0.47 1024 0.20
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表 7 最大重復(fù)次數(shù)對(duì)PPCA-SC復(fù)雜度的影響
信噪比(dB) 最大重復(fù)次數(shù) 時(shí)間復(fù)雜度 1.5 4 3522 2 2527 2.0 4 2486 2 2331 2.5 4 2126 2 2107
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表 8 分段數(shù)對(duì)PPCA-SC復(fù)雜度的影響
信噪比(dB) 分段數(shù) 時(shí)間復(fù)雜度 1.5 16 3522 8 3424 2.0 16 2466 8 2338 2.5 16 2126 8 2121
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