Jar Decoding: Non-Asymptotic Converse Coding Theorems, Taylor-Type Expansion, and Optimality

Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with discrete or continuous output (DIMC). Along the path of non-asymptotic analysis, in this paper, it is further shown that jar decoding is actually optimal up to the second order coding performance by establishing new non-asymptotic converse coding theorems, and determining the Taylor expansion of the (best) coding rate $R_n (\epsilon)$ of finite block length for any block length $n$ and word error probability $\epsilon$ up to the second order. Finally, based on the Taylor-type expansion and the new converses, two approximation formulas for $R_n (\epsilon)$ (dubbed "SO" and "NEP") are provided; they are further evaluated and compared against some of the best bounds known so far, as well as the normal approximation of $R_n (\epsilon)$ revisited recently in the literature. It turns out that while the normal approximation is all over the map, i.e. sometime below achievable bounds and sometime above converse bounds, the SO approximation is much more reliable as it is always below converses; in the meantime, the NEP approximation is the best among the three and always provides an accurate estimation for $R_n (\epsilon)$. An important implication arising from the Taylor-type expansion of $R_n (\epsilon)$ is that in the practical non-asymptotic regime, the optimal marginal codeword symbol distribution is not necessarily a capacity achieving distribution.Comment: submitted to IEEE Transaction on Information Theory in April, 201

Extremal RN/CFT in Both Hands Revisited

We study RN/CFT correspondence for four dimensional extremal Reissner-Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating black hole and make a geometric regularization of the 5d space-time. Both hands central charges are obtained correctly at the same time by Brown-Henneaux technique.Comment: 10 pages, no figur

Crystal structure of the 3C protease from South African Territories type 2 foot-and-mouth disease virus

The replication of foot-and-mouth disease virus (FMDV) is dependent on the virus-encoded 3C protease (3Cpro). As in other picornaviruses, 3Cpro performs most of the proteolytic processing of the polyprotein expressed from the single open reading frame in the RNA genome of the virus. Previous work revealed that the 3Cpro from serotype A – one of the seven serotypes of FMDV – adopts a trypsin-like fold. Phylogenetically the FMDV serotypes are grouped into two clusters, with O, A, C, and Asia 1 in one, and the three South African Territories serotypes, (SAT-1, SAT-2 and SAT-3) in another. We report here the cloning, expression and purification of 3C proteases from four SAT serotype viruses (SAT2/GHA/8/91, SAT1/NIG/5/81, SAT1/UGA/1/97, and SAT2/ZIM/7/83) and the crystal structure at 3.2 Å resolution of 3Cpro from SAT2/GHA/8/91)