The Asymptotic Generalized Poor-Verdu Bound Achieves the BSC Error Exponent at Zero Rate

A Generalized Poor-Verdu Error Bound for Multihypothesis Testing and the Channel Reliability Function

A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation with tilting parameter theta larger than or equal to 1, generalizes an earlier bound due the Poor and Verdu (1995). A sufficient condition is established under which the new bound (minus a multiplicative factor) provides the exact error probability in the limit of theta going to infinity. Examples illustrating the new bound are also provided. The application…

On the Evaluation of the Polyanskiy-Poor-Verdu Converse Bound for Finite Blocklength Coding in AWGN

A tight converse bound to channel coding rate in the finite block-length regime and under AWGN conditions was recently proposed by Polyanskiy, Poor, and Verdu (PPV). The bound is a generalization of a number of other classical results, and it was also claimed to be equivalent to Shannon's 1959 cone packing bound. Unfortunately, its numerical evaluation is troublesome even for not too large values of the block-length n. In this paper we tackle the numerical evaluation by compactly expressing the PPV converse bound in terms of non-central chi-squared distributions, and by evaluating those throug…

Decoder Ties Do Not Affect the Error Exponent of the Memoryless Binary Symmetric Channel

The generalized Poor-Verdu error lower bound established in [1] for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric channel (BSC), the minimum probability of error (under maximum likelihood decoding) has a relative deviation from the generalized bound that grows at most linearly in blocklength. This result directly implies that for arbitrary codes used over the BSC, decoder ties can only affect the subexponential behavior of the minimum probability of error.

Bayesian M-ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds are Tight

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are…

Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations

In this paper we provide new compact integral expressions and associated simple asymptotic approximations for converse and achievability bounds in the finite blocklength regime. The chosen converse and random coding union bounds were taken from the recent work of Polyanskyi-Poor-Verdu, and are investigated under parallel AWGN channels, the AWGN channels, the BI-AWGN channel, and the BSC. The technique we use, which is a generalization of some recent results available from the literature, is to map the probabilities of interest into a Laplace integral, and then solve (or approximate) the integr…

用于单次信息论的成对错误概率框架

A Pairwise-Error-Probability Framework for One-Shot Information Theory

该研究提出基于成对错误概率的单次信息论信道编码框架，推导相关变分恒等式，可恢复经典单次界，通过数值示例验证其效果。