Refinement of the random coding bound

An improved pre-factor for the random coding bound is proved. Specifically, for channels with critical rate not equal to capacity, if a regularity condition is satisfied (resp. not satisfied), then for any $\epsilon >0$ a pre-factor of $O(N^{-\frac{1}{2}\left( 1 - \epsilon + \bar{\rho}^\ast_R \right)})$ (resp. $O(N^{-\frac{1}{2}})$) is achievable for rates above the critical rate, where $N$ and $R$ is the blocklength and rate, respectively. The extra term $\bar{\rho}^\ast_R$ is related to the slope of the random coding exponent. Further, the relation of these bounds with the authors' recent refinement of the sphere-packing bound, as well as the pre-factor for the random coding bound below the critical rate, is discussed.Comment: Submitted to IEEE Trans. Inform. Theor

The third-order term in the normal approximation for singular channels

For a singular and symmetric discrete memoryless channel with positive dispersion, the third-order term in the normal approximation is shown to be upper bounded by a constant. This finding completes the characterization of the third-order term for symmetric discrete memoryless channels. The proof method is extended to asymmetric and singular channels with constant composition codes, and its connection to existing results, as well as its limitation in the error exponents regime, are discussed.Comment: Submitted to IEEE Trans. Inform. Theor

A failed case of percutaneous septal closure of fenestrated atrial septal defect

A patient presenting with a history of palpitation and exertional dyspnea was initially diagnosed with two separate secundum-type atrial septal defects by transesophageal echocardiography. Subsequent transesophageal echocardiography, after failure of closure with two separate closure devices, showed another defect and an ongoing left to right shunt. During surgery, more defects were observed. The defects were successfully repaired using pericardial patch without incident. (Cardiol J 2011; 18, 1: 92-93

Moderate Deviations And Exact Asymptotics In Channel Coding

Investigation of the data rate, blocklength and error probability interplay for the optimum block code(s) on a discrete memoryless channel is a fundamental problem of information theory. Because of the intricacy of the problem, it is ubiquitous to allow blocklength to grow unboundedly, which, in turn, gives informative optimality results. Although there are classical asymptotic regimes to investigate this interplay, they have certain limitations. This thesis is about two new asymptotics in channel coding, proposed to address these limitations. In moderate deviations, we consider the optimal error performance of the sequence of codes with rates increasing to the capacity with a speed between the classical asymptotic regimes of error exponents and normal approximation and prove that error probability vanishes sub-exponentially fast with a rate related to the dispersion of the channel. This conclusion is in contrast with the classical asymptotic regimes, in which either error probability vanishes or rate increases to the capacity, but not simultaneously. We believe that this contrast makes moderate deviations more relevant to practical code design, since the goal of the channel coding is to attain a rate that is close to capacity and an error probability that is close to zero. In exact asymptotics, we concentrate on the sub-exponential factors of the wellknown exponentially decaying bounds on the error probability to improve their orders. The reason of this quest is the fact that the exponent of these bounds vanishes as rate approaches the capacity, which, in turn, makes the sub-exponential terms to play a sig- nificant role in the approximation of the error probability for this range of rates. The sharpened orders of the sub-exponential factors of these refinements are close to each other in general, and are equal for symmetric channels. Moreover, we reveal a phase transition of the optimal order of the pre-factor for this class of channels