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Extrinsic Jensen–Shannon Divergence: Applications to Variable-Length Coding

机译：外在延森-香农散度：可变长度编码的应用

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摘要

This paper considers the problem of variable-length coding over a discrete memoryless channel with noiseless feedback. This paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen–Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide nonasymptotic upper bounds on the expected code length. This paper presents strictly positive lower bounds on EJS divergence, and hence nonasymptotic upper bounds on the expected code length, for the following two coding schemes: 1) variable-length posterior matching and 2) MaxEJS coding scheme that is based on a greedy maximization of the EJS divergence. As an asymptotic corollary of the main results, this paper also provides a rate–reliability test. Variable-length coding schemes that satisfy the condition(s) of the test for parameters and are guaranteed to achieve a rate and an error exponent . The results are specialized for posterior matching and MaxEJS to obtain deterministic one-phase coding schemes achieving capacity and optimal error exponent. For the special case of symmetric binary-input channels, simpler deterministic schemes of optimal performance are proposed and analyzed.
机译：本文考虑具有无噪声反馈的离散无记忆通道上可变长度编码的问题。本文提供了对该问题的随机控制观点，该问题的解决方案是通过新提出的对称散度（称为外部Jensen-Shannon（EJS）散度）来分析的。结果表明，EJS散度上的严格正下限提供了预期代码长度上的非渐近上限。本文针对以下两种编码方案，给出了EJS散度的严格正下界，以及预期代码长度的非渐近上限：1）可变长度后验匹配和2）基于贪婪最大化的MaxEJS编码方案EJS的分歧。作为主要结果的渐近推论，本文还提供了速率可靠性测试。满足参数测试条件并保证获得速率和误差指数的可变长度编码方案。结果专门用于后验匹配和MaxEJS，以获得可实现容量和最佳误差指数的确定性单相编码方案。对于对称二进制输入通道的特殊情况，提出并分析了最优性能的更简单确定性方案。

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