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首页> 外文期刊>Information Theory, IEEE Transactions on >Interactive Encoding and Decoding Based on Binary LDPC Codes With Syndrome Accumulation
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Interactive Encoding and Decoding Based on Binary LDPC Codes With Syndrome Accumulation

机译：具有二进制累积量的基于二进制LDPC码的交互式编码和解码

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摘要

Interactive encoding and decoding based on binary low-density parity-check codes with syndrome accumulation (SA-LDPC-IED) is proposed and investigated. Assume that the source alphabet is ${bf GF}(2)$, and the side information alphabet is finite. It is first demonstrated how to convert any classical universal lossless code ${cal C}_{n}$ (with block length $n$ and side information available to both the encoder and decoder) into a universal SA-LDPC-IED scheme. It is then shown that with the word error probability approaching 0 subexponentially with $n$ , the compression rate (including both the forward and backward rates) of the resulting SA-LDPC-IED scheme is upper bounded by a functional of that of ${cal C}_{n}$, which in turn approaches the compression rate of ${cal C}_{n}$ for each and every individual sequence pair $(x^{n}, y^{n})$ and the conditional entropy rate ${rm H} (X vert Y)$ for any stationary, ergodic source and side information $(X, Y)$ as the average variable node degree ${bar {l}}$ of the underlying LDPC code increases without bound. When applied to the class of binary source and side information $(X, Y)$ correlated through a binary symmetrical channel with crossover probability unknown to both the encoder and decoder- the resulting SA-LDPC-IED scheme can be further simplified, yielding even improved rate performance versus the bit error probability when ${bar {l}}$ is not large. Simulation results (coupled with linear time belief propagation decoding) on binary source-side information pairs confirm the theoretic analysis and further show that the SA-LDPC-IED scheme consistently outperforms the Slepian–Wolf coding scheme based on the same underlying LDPC code. As a by-product, probability bounds involving LDPC established in the course are also interesting on their own and expected to have implications on the performance of LDPC for channel coding as well.
机译：提出并研究了基于带有校验子累积的二进制低密度奇偶校验码的交互式编码和解码（SA-LDPC-IED）。假设源字母是 $ {bf GF}（2）$ ，并且辅助信息字母是有限的。首次演示了如何转换任何经典的通用无损代码 $ {cal C} _ {n} $ （具有块长度） $ n $ 以及可用于编码器和解码器的辅助信息）转换为通用SA-LDPC-IED方案。然后表明，在 $ n $ 的情况下，单词错误概率接近指数地接近0，压缩率（包括正向和SA-LDPC-IED方案的反向速率）是 $ {cal C} _ {n} $ ，其反而接近 $ {cal C} _ {n} $ 的压缩率每个单独的序列对 $（x ^ {n}，y ^ {n}）$ 和条件熵率 $ {rm H}（X vert Y）$ ，用于获取任何平稳的，遍历的来源和辅助信息 $（X，Y）$ 作为平均变量节点度 $ {bar {l}} $ 无限增加。当应用于二进制源和辅助信息的类别时， $（X，Y）$ 通过具有交叉的二进制对称通道进行关联编码器和解码器均未知的概率-可以进一步简化所得的SA-LDPC-IED方案，与 $ {bar {l}} $ 不大。对二进制源侧信息对的仿真结果（与线性时间置信度传播解码结合）证实了理论分析，并进一步表明，基于相同的基础LDPC码，SA-LDPC-IED方案始终优于Slepian-Wolf编码方案。作为副产品，在课程中建立的涉及LDPC的概率范围本身也很有趣，并且有望对LDPC的信道编码性能产生影响。

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