混合信道下LDPC码稳定条件分析及度序列优化

doi:10.11959/j.issn.1000-436x.2016188

摘要/Abstract

摘要：

在高斯噪声和随机删除同时存在的背景下，提出LDPC码度序列的稳定收敛条件，理论证明了高斯信道下阈值较高的度序列不适用于混合信道，并仿真验证了该结论。将随机粒子群算法和模拟退火算法相结合，不同删除概率下寻找到了一些高阈值混合信道的度序列，删除概率为40%时，度序列信噪比阈值最大可提高1.615 9 dB，适用于光记录、伴随窄带阻塞干扰的跳频通信等混合信道环境。

关键词: 低密度奇偶校验码, 混合信道, 高斯近似, 随机粒子群优化, 模拟退火

Abstract:

Under the circumstance that white Gaussian noise and random erasures exist all at once,the stability condition for LDPC codes over mixed channel was proposed.And it was proved that a good degree sequence of LDPC codes was not optimized over mixed channel.It can also be proved by simulation.The random particle swarm optimization (RPSO) and simulated annealing (SA) algorithm were combined to find some capacity-approaching degree sequences over mixed channel with different erasure probabilities.The threshold of signal-to-noise ratio improves 1.615 9 dB than that of the classical degree sequences calculated by Gaussian approximation over mixed channel.These degree sequences are optimal for optical recording and frequency-hopping communication with narrow-band interference.

Key words: low density parity check codes, mixed channel, Gaussian approximation, simulated annealing

孙康宁,马林华,茹乐,范文同,胡星,黄绍城. 混合信道下LDPC码稳定条件分析及度序列优化[J]. 通信学报, 2016, 37(9): 168-174.

Kang-ning SUN,Lin-hua MA,Le RU,Wen-tong FAN,Xing HU,Shao-cheng HUANG. Analysis of stability condition for LDPC codes and optimizing degree sequences over mixed channel[J]. Journal on Communications, 2016, 37(9): 168-174.

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参考文献 16

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变量节点最大度数	λ₂	λ₃	λ₄	λ₅	λ₆	λ₇	λ₈	λ₉	λ₁₀
6	0.348 772	0.203 68			0.447 548
7	0.326 726	0.240 377				0.432 897
8	0.305 478	0.255 63					0.438 892
9	0.290 06	0.257 019	0.000 621 2					0.452 921
10	0.263 796	0.284 713							0.451 491
11	0.253 568	0.239 817	0.065 674 8
12	0.241 166	0.239 673
变量节点最大度数	λ₁₁	λ₁₂	ρ₆	ρ₇	ρ₈	σ	σ^*	ΔSNR /dB
6			0.712 684	0.287 316		0.759 3	0.739 5	0.528 5
7			0.495 713	0.504 287		0.765 0	0.762 7	0.060 2
8			0.363 765	0.636 235		0.768 3	0.767 8	0.013 0
9				0.924 087	0.075 913	0.774 2	0.771 3	0.075 1
10				0.718 439	0.281 561	0.777 3	0.773 3	0.103 2
11	0.440 940 2			0.590 058	0.409 942	0.777 8	0.775 2	0.067 0
12		0.441 727 1		0.393 068	0.606 932	0.778 7	0.776 8	0.048 9

变量节点最大度数	λ₂	λ₃	λ₄	λ₅	λ₆	λ₇	λ₈	λ₉	λ₁₀
6	0.360 024	0.197 862			0.442 114
7	0.339 428	0.237 5				0.423 072
8	0.328 037	0.243 873					0.428 09
9	0.291 013	0.263 852	0.000 621 2					0.444 513 8
10	0.270 235	0.285 333							0.444 432
11	0.278 456	0.229 394		0.091 927 3
12	0.251 084	0.285 552
变量节点最大度数	λ₁₁	λ₁₂	ρ₆	ρ₇	ρ₈	σ	σ^*	ΔSNR /dB
6			0.712 684	0.287 316		0.759 3	0.739 5	0.528 5
7			0.495 713	0.504 287		0.765 0	0.762 7	0.060 2
8			0.363 765	0.636 235		0.768 3	0.767 8	0.013 0
9				0.924 087	0.075 913	0.774 2	0.771 3	0.075 1
10				0.718 439	0.281 561	0.777 3	0.773 3	0.103 2
11	0.400 222 7			0.590 058	0.409 942	0.777 8	0.775 2	0.067 0
12		0.463 364		0.393 068	0.606 932	0.778 7	0.776 8	0.048 9

变量节点最大度数	λ₂	λ₃	λ₄	λ₅	λ₆	λ₇	λ₈	λ₉	λ₁₀
6	0.376 12	0.183 439			0.440 441
7	0.351 341	0.214 155				0.434 504
8	0.329 475	0.250 915					0.419 61
9	0.310 765	0.258 623						0.430 612
10	0.281 642	0.282 192							0.436 166
11	0.285 014	0.255 886		0.013 929 6
12	0.277 149	0.175 268	0.128 691
变量节点最大度数	λ₁₁	λ₁₂	ρ₆	ρ₇	ρ₈	σ	σ^*	ΔSNR /dB
6			0.774 876	0.225 124		0.654 4	0.631 5	0.712 4
7			0.491 677	0.508 323		0.661 1	0.654 8	0.191 5
8			0.317 369	0.682 631		0.666 2	0.660 1	0.184 0
9			0.161 002	0.838 998		0.668 9	0.662 7	0.186 2
10				0.811 591	0.188 409	0.671 7	0.664 3	0.221 6
11	0.445 170 4			0.705 986	0.294 014	0.673 2	0.665 9	0.218 1
12		0.418 892		0.394 167	0.605 833	0.675 7	0.667 2	0.253 2

变量节点最大度数	λ₂	λ₃	λ₄	λ₅	λ₆	λ₇	λ₈	λ₉	λ₁₀
6	0.405 845	0.163 717			0.430 438
7	0.377 761	0.197 289				0.424 941
8	0.350 37	0.227 777					0.421 859
9	0.324 075	0.253 083						0.422 842
10	0.301 084	0.252 888							0.446 028
11	0.308 276	0.182 559	0.106 238
12	0.277 534	0.272 35
变量节点最大度数	λ₁₁	λ₁₂	ρ₆	ρ₇	ρ₈	σ	σ^*	ΔSNR /dB
6			0.913 922	0.086 078		0.508 9	0.469 4	1.615 9
7			0.622 401	0.377 599		0.517 9	0.501 8	0.631 6
8			0.380 694	0.619 306		0.524 1	0.509 1	0.580 8
9			0.161 002	0.838 998		0.528	0.510 5	0.674 1
10				0.842 852	0.157 148	0.532 8	0.512 1	0.792 5
11	0.402 927			0.789 044	0.210 956	0.533 1	0.513 7	0.741 4
12		0.450 116		0.568 513	0.431 487	0.534 1	0.514 8	0.736 1