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首页> 外文期刊>Information Theory, IEEE Transactions on >High-Rate Self-Synchronizing Codes
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High-Rate Self-Synchronizing Codes

机译：高速自同步代码

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摘要

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error tolerance that generate binary and ternary self-synchronizing codes.
机译：在附加噪声存在下的自同步可以通过分配每个码字的一定数量的比特作为同步标记来实现。集合的不同系统是组合设计，其以这样的方式指定同步标记在码字中的位置，使得可以将所得的容错自同步码实现为线性码的同集。理想情况下，对于给定的代码长度，字母大小和容错能力，集合的差分系统应牺牲尽可能少的位。但是，当噪声水平相对较低时，似乎很难在已知范围内达到最佳。实际上，大多数已知的最佳差分集系统都用于异常嘈杂的信道，需要大量的比特来进行同步。为了解决这个问题，我们提出了用于差分集系统的构造，其允许较高的信息速率，同时只在很小的程度上牺牲了最优性。我们的构造利用集合的最佳差分系统作为成分，并且当仔细应用时，会生成具有较高信息率的渐近最佳系统。我们还给出了具有高信息率和容错能力的最佳差分系统的直接构造，该系统生成二进制和三进制自同步代码。

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