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首页> 外文期刊>Information Theory, IEEE Transactions on >Linear Interactive Encoding and Decoding for Lossless Source Coding With Decoder Only Side Information
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Linear Interactive Encoding and Decoding for Lossless Source Coding With Decoder Only Side Information

机译：仅解码器附带信息的无损源编码的线性交互式编码和解码

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摘要

Linear interactive encoding and decoding (IED) for near lossless source coding with decoder only side information is considered, where the interactive encoder uses linear codes (described by parity-check matrices over a finite field ${cal X}$) for encoding. It is first demonstrated how to convert any classical universal lossless code ${cal C}_n$ (with block length $n$ and with side information available to both the encoder and decoder) into a universal random linear IED scheme based on Gallager's parity check ensemble. It is then shown that there is no performance loss by restricting IED to linear IED, and that the universal random linear IED scheme based on Gallager's parity check ensemble achieves essentially the same rate performance as does ${cal C}_n$ for each and every individual sequence pair $(x^n, y^n)$ while the word decoding error probability goes to $0$ as $n to infty$ . Define the density of a linear IED scheme as the percentage of nonzero entries in its parity-check matrix. To reduce the encoding complexity of linear IED, low density linear IED is further investigated in terms of the trade-off among its rate, decoding error probability, and density.
机译：考虑了仅具有解码器辅助信息的用于近乎无损源编码的线性交互式编码和解码（IED），其中交互式编码器使用线性代码（由有限域$ {cal X} $上的奇偶校验矩阵描述）进行编码。首次演示了如何根据Gallager奇偶校验将任何经典的通用无损代码$ {cal C} _n $（具有块长$ n $，且编码器和解码器均具有辅助信息）转换为通用随机线性IED方案合奏。然后表明，通过将IED限制为线性IED不会造成性能损失，并且基于Gallager奇偶校验集成的通用随机线性IED方案在每个方面都实现了与$ {cal C} _n $相同的速率性能。单个序列对$（x ^ n，y ^ n）$，而字解码错误的概率从$ n到infty $变为$ 0 $将线性IED方案的密度定义为其奇偶校验矩阵中非零条目的百分比。为了降低线性IED的编码复杂度，我们进一步研究了低密度线性IED的速率，解码错误概率和密度之间的权衡。

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