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首页> 外文期刊>IEEE Transactions on Information Theory >Near-optimal limited-search detection on ISI/CDMA channels and decoding of long convolutional codes
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Near-optimal limited-search detection on ISI/CDMA channels and decoding of long convolutional codes

机译：ISI / CDMA信道上的近最佳有限搜索检测和长卷积码的解码

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摘要

We derive an upper bound on the bit-error probability (BEP) in limited-search detection over a finite interference channel. A unified channel model is presented; this includes finite-length intersymbol interference channels and multiuser CDMA channels as two special cases. We show that the BEP of the M-algorithm (MA) is bounded from above by the sum of three terms: an upper bound on the error probability of the Viterbi (1967) algorithm (VA) detection given by Forney Jr. (1972), and upper bounds on the error probabilities of two types of erroneous decision caused by the correct path loss event. We prove that error propagation (in terms of the mean recovery step number) is finite for all finite interference channels. The convergence and asymptotic behavior of the upper bounds are studied. The results show that, if a channel satisfies certain mild conditions, all series in the bounds are convergent. One of the key results is that, for any finite interference channel satisfying certain mild conditions. the asymptotic BEP of the MA is bounded by the same upper and lower bounds (which have the same asymptotical behavior) as those for the VA if the correct path loss probability is smaller than that of the VA. Furthermore, we extend the above results to near optimally decode long convolutional codes in a short packet format (about 200-300 bits). We present a nonsorting combined M/T algorithm and showed that the M/T algorithm with M<2(/sup d/free//sup n/) and T<(d/sub free/E/sub b/) can near-optimally decode the code. We also propose a hierarchical decoding algorithm (HDA) to further cut down the average decoding complexity. Numerical results show that the bounds are reasonably tight. The HDA can achieve a performance within about 0.8 dB of the sphere-packing lower bound for a packet error rate of 10/sup -4/ and a packet length below 200 bits, which is the best reported decoding performance so far for block sizes from 100 to 200 bits.
机译：我们在有限干扰信道上的有限搜索检测中得出误码概率（BEP）的上限。提出了统一的渠道模型；这包括有限长度的符号间干扰信道和多用户CDMA信道，这是两种特殊情况。我们显示M算法（MA）的BEP由三个项的总和从上方界定：Forney Jr.（1972）给出的Viterbi（1967）算法（VA）检测的错误概率上限。 ，以及由正确的路径丢失事件引起的两种错误决策的错误概率的上限。我们证明，对于所有有限的干扰信道，误差传播（就平均恢复步长而言）是有限的。研究了上限的收敛性和渐近行为。结果表明，如果通道满足某些温和条件，则边界中的所有序列都是收敛的。关键结果之一是，对于满足某些温和条件的任何有限干扰信道。如果正确的路径损耗概率小于VA，则MA的渐近BEP受与VA相同的上限和下限（具有相同的渐近行为）限制。此外，我们将上述结果扩展为以短分组格式（大约200-300位）对长卷积码进行近乎最佳的解码。我们提出了一种非排序的组合M / T算法，并证明了M / T算法具有M <2（/ sup d / free // sup n /）和T <（d / sub free / E / sub b /）/ n可以优化代码。我们还提出了一种分层解码算法（HDA），以进一步降低平均解码复杂度。数值结果表明边界是合理的。对于10 / sup -4 /的数据包错误率和200位以下的数据包长度，HDA可以达到球面压缩下限约0.8 dB内的性能，这是迄今为止针对以下数据块大小报告的最佳解码性能100至200位。

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