本文選題：極化碼　切入點：高斯近似　出處：《北京郵電大學(xué)》2015年碩士論文

【摘要】：自1948年香農(nóng)提出信道編碼理論以來,信道編碼界的研究者們沿著香農(nóng)所指引的方向,向可靠性極限(香農(nóng)限)逼近。Turbo碼和LDPC碼在BPSK調(diào)制下已經(jīng)達(dá)到了距離香農(nóng)限不到0.1dB的優(yōu)異性能。然而,這些結(jié)果都是在碼長極長的情況下通過仿真得到,并無嚴(yán)格的理論可達(dá)性證明。2009年由Erdal Arikan中提出的極化碼是第一種被嚴(yán)格證明可以達(dá)到信道容量的構(gòu)造性的信道編碼方法,極化碼以較低的編譯碼復(fù)雜度及其容量可達(dá)性受到學(xué)術(shù)界的廣泛關(guān)注。這種新的編碼方式可以對編碼和調(diào)制進(jìn)行聯(lián)合優(yōu)化,不僅可以逼近信道容量,同時可以提高頻譜效率。此外由于其結(jié)構(gòu)簡單規(guī)則,可采用并行譯碼架構(gòu),能進(jìn)一步提高吞吐效率。極化碼以其眾多方面的性能和優(yōu)勢有望在未來通信系統(tǒng)中得到重要應(yīng)用。 本文主要關(guān)注和研究極化碼的實用化譯碼技術(shù),重點研究AWGN信道下極化碼的串行抵消(Successive Cancellation, SC)量化譯碼算法及相關(guān)優(yōu)化算法。主要包括三個研究點和創(chuàng)新點： 首先,在AWGN信道下研究極化碼的基本量化譯碼算法,使其在極化碼硬件設(shè)計方面更具實用價值和指導(dǎo)意義。本文在高斯近似方法的指導(dǎo)下,提出了基于最小均方誤差、最大容量和最大截止速率三種量化準(zhǔn)則的SC量化譯碼算法。其次,在最大截止速率量化準(zhǔn)則的基礎(chǔ)之上,文中對浮點條件下的高斯近似方法進(jìn)行改進(jìn),使其能夠在量化譯碼條件下對極化碼進(jìn)行構(gòu)造,并對量化SC譯碼算法下極化碼的誤幀率上界進(jìn)行估計。最后,基于改進(jìn)高斯近似方法,本文進(jìn)一步提出SC量化譯碼下的最優(yōu)量化比特數(shù)搜索算法,壓縮不同程度的極化子信道所用的量化比特數(shù),從而降低量化譯碼的平均量化比特數(shù)。此外,本文還從對數(shù)概率域和對數(shù)似然率域兩方面對列表譯碼算法的量化問題進(jìn)行闡述和初步研究,并給出了簡單可行的量化譯碼方案。 仿真分析表明,在文中提出的三種量化準(zhǔn)則下,SC量化譯碼算法采用6bit均勻量化足以達(dá)到浮點譯碼性能,且改進(jìn)的高斯近似方法可以準(zhǔn)確估計量化SC譯碼算法的誤塊率上界,在最優(yōu)量化比特搜索算法下,平均量化比特數(shù)可以降低到4.5bit。而對于列表譯碼算法的量化,基于對數(shù)概率域的量化方法在信道一側(cè)采用4bit量化,逐級增加1bit的量化方式可以達(dá)到浮點譯碼性能。而基于對數(shù)似然率的量化譯碼方法對所有似然率進(jìn)行7bit的均勻量化即可達(dá)到浮點譯碼性能,該方法更具實用性。
[Abstract]:Since Shannon put forward channel coding theory in 1948, researchers in channel coding field have followed Shannon's direction. Approaching to the reliability limit (Shannon limit). Turbo code and LDPC code have achieved the excellent performance of distance Shannon limit less than 0.1dB under BPSK modulation. However, these results are obtained by simulation under the condition of extremely long code length. The polarimetric code proposed by Erdal Arikan in 2009 is the first channel coding method which is strictly proved that it can achieve channel capacity. Polarization codes have attracted much attention in academia for their low encoding and decoding complexity and their capacity reachability. This new coding scheme can be combined to optimize coding and modulation, and it can not only approximate the channel capacity, but also improve the performance of polarimetric codes. In addition, the parallel decoding architecture can be used to further improve the throughput efficiency because of its simple structure. Polarization codes are expected to be important applications in future communication systems due to their performance and advantages in many aspects. This paper mainly focuses on the practical decoding technology of polarimetric codes, focusing on the serial cancellation of polarimetric codes over AWGN channels and the related optimization algorithms, including three research points and innovations:. First of all, the basic quantization decoding algorithm of polarization code is studied in AWGN channel, which makes it more practical and instructive in the design of polarization code hardware. Under the guidance of Gao Si's approximation method, this paper proposes a new algorithm based on minimum mean square error (MMSE). SC quantization decoding algorithm for maximum capacity and maximum cut-off rate quantization criterion. Secondly, on the basis of the maximum cut-off rate quantization criterion, the Gao Si approximation method under floating point condition is improved in this paper. It can construct the polarization code under the condition of quantization decoding, and estimate the upper bound of the frame error rate of the polarization code under the quantization SC decoding algorithm. Finally, based on the improved Gao Si approximation method, In this paper, we further propose an optimal quantization bit number search algorithm for SC quantization decoding, which compresses the quantized bits used in different polarization subchannels, thus reducing the average quantization bit number of quantization decoding. In this paper, the quantization problem of list decoding algorithm is discussed and studied from two aspects of logarithmic probability domain and logarithmic likelihood rate domain, and a simple and feasible quantization decoding scheme is given. Simulation results show that 6bit uniform quantization is sufficient to achieve floating-point decoding performance under the three quantization criteria proposed in this paper, and the improved Gao Si approximation method can accurately estimate the upper bound of block error rate of quantization SC decoding algorithm. Under the optimal quantization bit search algorithm, the average quantized bit number can be reduced to 4.5 bits.For the quantization of list decoding algorithm, the quantization method based on logarithmic probability domain uses 4bit quantization on the channel side. The performance of floating-point decoding can be achieved by incrementing the quantization of 1bit step by step, while the uniform quantization of all likelihood rates by quantization based on logarithmic likelihood can achieve the performance of floating-point decoding, which is more practical.
【學(xué)位授予單位】：北京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：TN911.22

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