Polar martingales of maximal spread
نویسنده
چکیده
This paper investigates polar codes for q-ary input channels using other kernels than [ 1 0 1 1 ] to construct the generator matrix. The kernel is optimized by maximizing the spread of the polar martingale and it is shown that in certain cases, the resulting construction has a significantly improved error probability (even at small block length like n = 1024).
منابع مشابه
Maximal Partial Spreads of Polar Spaces
Some constructions of maximal partial spreads of finite classical polar spaces are provided. In particular we show that, for n > 1, H(4n−1, q2) has a maximal partial spread of size q2n + 1, H(4n + 1, q2) has a maximal partial spread of size q2n+1 + 1 and, for n > 2, Q+(4n − 1, q), Q(4n − 2, q), W(4n − 1, q), q even, W(4n − 3, q), q even, have a maximal partial spread of size qn + 1.
متن کاملA Systematic Martingale Construction With Applications to Permutation Inequalities
We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by ...
متن کاملSharp Maximal Inequalities for Conditionally Symmetric Martingales and Brownian Motion
Let B = {Bt)t>0 be a standard Brownian motion. For c > 0, k > 0 , let T(c, k) = inî{t > 0: maxs<í Bs cBt > k} , T"(c,k)= inf{r>0: max^, \BS\ c\B,\ > k} . We show that for c > 0 and k > 0, both T(c, k) and T*{c, k) axe finite almost everywhere. Moreover, T(c, k) and T*(c, k) e L if and only if c < pKp 1) for p > 1 , and for all c > 0 when p < 1 . These results have analogues for simple random wa...
متن کاملThe Maximum Size of a Partial Spread in H(4n+1, q2) is q2n+1+1
We prove that in every finite Hermitian polar space of odd dimension and even maximal dimension ρ of the totally isotropic subspaces, a partial spread has size at most qρ+1 + 1, where GF (q2) is the defining field. This bound is tight and is a generalisation of the result of De Beule and Metsch for the case ρ = 2.
متن کاملA maximal inequality for continuous martingales andM - estimation in a Gaussian white noise model
Some suucient conditions to establish the rate of convergence of certain M-estimators in a Gaussian white noise model are presented. They are applied to some concrete problems, including jump point estimation and non-parametric maximum likelihood estimation, for the regression function. The results are shown by means of a maximal inequality for continuous martingales and some techniques develop...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012