【摘要】：Tanner圖中的環(huán)分布影響著低密度校驗(yàn)碼(LDPC,low-density parity-check code)譯碼算法的誤碼率性能,為快速計(jì)算出Tanner圖中短環(huán)的數(shù)目,提出一種逐邊遞推基于矩陣運(yùn)算的算法。首先定義5種基本圖結(jié)構(gòu),算法在實(shí)施過(guò)程中可實(shí)現(xiàn)結(jié)構(gòu)間的遞推。與之前的研究工作相比,該算法對(duì)于同一環(huán)長(zhǎng)提供多種方法進(jìn)行計(jì)算,得到相同的計(jì)算結(jié)果,進(jìn)一步證實(shí)算法的正確性。新算法不僅能計(jì)算出總的環(huán)數(shù),還能給出每一條邊參與的環(huán)數(shù)。該算法將時(shí)間復(fù)雜度從正比于碼長(zhǎng)N的3次方降為正比于碼長(zhǎng)的平方與變量節(jié)點(diǎn)平均度數(shù)D的乘積(DN)。對(duì)于大多數(shù)的LDPC碼,計(jì)算環(huán)長(zhǎng)為g、g+2、g+4的環(huán)數(shù)需要的時(shí)間僅為數(shù)秒。
[Abstract]:The ring distribution in Tanner graph affects the bit error rate (BER) performance of low density check code (LDPC,low-density parity-check code) decoding algorithm. In order to quickly calculate the number of short rings in Tanner graph, an edge-by-side recurrence algorithm based on matrix operation is proposed. Firstly, five basic graph structures are defined, and the algorithm can realize the recurrence between structures in the process of implementation. Compared with the previous research work, the algorithm provides a variety of methods for the same ring length to calculate, and the same calculation results are obtained, which further verifies the correctness of the algorithm. The new algorithm can not only calculate the total number of rings, but also give the number of rings in which each edge participates. The algorithm reduces the time complexity from the third power proportional to the code length N to the product of the square of the code length and the mean degree D of the variable node. (DN). For most LDPC codes, it takes only a few seconds to calculate the ring length g 2 and the ring number of g 4 only a few seconds.
【作者單位】： 國(guó)電南瑞科技股份有限公司;東南大學(xué)信息科學(xué)與工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(No.61233007)~~
【分類(lèi)號(hào)】：TN911.22

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