通信工程文献翻译——摘要——在这篇文章里，我们针对带交织的并行和串行级联码的自由码距的计算提出了一种新的算法，研究出来的参数主要用来使编码达到很高的信噪比，自由码距允许我们去分析估计最低错误率，这样就能够避免级联码在应用中超过最低误码率。这种算法以新的约束子码为基础，而且允许在不限制输入重量的前提下的多约束远距离的计算（例如：对于码率为1/3的Turbo码及约束长度为3568时，自由码距达到40）。相关的实际应用：1）关于太空遥测的新型的空间数据系统咨询委员会（CCSDS）2）关于第三代个人通信的新型UMTS/3GPP标准。其他相关方面，像关于自由码距的研究把Turbo码分成小或中等约束长度及并行和串行连接行为的比较也将在本文中给以讨论。

术语索引——级联码；自由码距；性能约束；Turbo码；UMTS

简介

在编码理论的这个特殊领域中，交织级联码代表了一种很大的进步。并行交织级联卷积码（Turbo码）[1]，包括通过交织器并行连接的简单二进制卷积码，Turbo码被广泛接受，并且他们的产品在许多国家标准上都有所提高 [像太空遥测的空间数据系统咨询委员会（CCSDS）[2]；个人通信的UMTS/3GPP标准[3]；电视广播的ETSI标准及其他的[4]]。最先在参考文献[5]中提出的串行级联卷积码，在许多情况下可能优于Turbo玛，尤其是低的误码率（BERS）和低的误信率（FERS）。

PCCCS和SCCCS都可以通过重复由卷积码组成的BCJR算法（又称前后循环或APP算法）在接收端得到译码[6]，通过这个译码算法，在低或中等信噪比的前提下，这种译码表现的很好（非常接近仙农限），尽管如此，我们都知道在要求很高信噪比的情况下，这种译码表现的不是很理想[7]。

在这个领域，任何一个二进制码都以它的自由码距（两个码字之间的最小汉明码距，它与一个线性码非零码字的最小汉明码重一致）和多重性为主流。即使有非常大的交织长度N，交织级联码也可能只有非常低的自由码距[7]。由于错误平层受自由码距的压迫，所以使误码率BER在低SNRs水平减小之后也由曲线渐渐变平的......

Abstract—In this paper, we present a new algorithm for computing the free distance free of parallel and serially concatenated codes with interleavers, the parameter that dominates the code per-formance at very high signal-to-noise ratios (SNRs). The knowledge of free allows one to analytically estimate the error floor, which may prevent the use of concatenated codes in applications requiring very low error rates. The algorithm is based on the new notion of constrained subcodes, and permits the computation of large distances for large interleavers without a constraint on the input sequence weight (e.g., up to free = 40 for a rate-1/3 turbo code with interleaver length = 3568). Applications to practical cases of relevant interest, i.e., 1) the new Consultative Committee for Space Data Systems (CCSDS) standard for deep-space telemetry and 2)

the new UMTS/3GPP standard for third-generation personal communications, are presented here for the first time. Other related aspects, like a study on the free distance distribution of turbo codes with small/medium interleaver length, and a comparison between parallel and serial concatenation behavior, are also discussed in the paper.

Index Terms—Concatenated codes, free distance, performance bounds, turbo codes, UMTS.

CONCATENATED codes with interleavers represent a great advancement in coding theory for their exceptional performance. Parallel concatenated convolutional codes with interleavers (PCCCs, or turbo codes), introduced in [1],consist of simple binary convolutional codes connected in parallel through an interleaver. Turbo codes are obtaining a wide acceptance and their introduction in many international standards [like the Consultative Committee for Space Data Systems (CCSDS) standard for deep-space telemetry [2], the UMTS/3GPP standard for personal communications......