Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity
Least Squares Superposition Codes of Moderate Dictionary Size Are Reliable at Rates up to Capacity
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DOI：
10.1109/tit.2012.2184847
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发表时间：
2012-05-01
影响因子：
2.5
通讯作者：
Barron, Andrew R.
中科院分区：
文献类型：
--
作者：
Joseph, Antony;Barron, Andrew R.
对于具有平均码字功率约束的加性高斯白噪声信道，分析了码字为稀疏叠加的编码方法，即给定设计的向量子集的线性组合，通过选择子集对可能的消息进行索引。解码是通过最小二乘（最大似然），根据假设的码字形式（设计元素的线性组合）进行定制。在香农容量以下的所有速率下，通信是可靠的，误差概率呈指数级小。
For the additive white Gaussian noise channel with average codeword power constraint, coding methods are analyzed in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design, with the possible messages indexed by the choice of subset. Decoding is by least squares (maximum likelihood), tailored to the assumed form of codewords being linear combinations of elements of the design. Communication is shown to be reliable with error probability exponentially small for all rates up to the Shannon capacity.