Polarization Codes: Characterization of Exponent, Bounds, and Constructions
نویسندگان
چکیده
Polarization codes were recently introduced by Arıkan. They achieve the capacity of arbitrary symmetric binaryinput discrete memoryless channels (and even extensions thereof) under a low complexity successive decoding strategy. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the 2× 2 matrix
منابع مشابه
Strong exponent bounds for the local Rankin-Selberg convolution
Let $F$ be a non-Archimedean locally compact field. Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$. We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$. Using the Langlands...
متن کاملOn Error Exponents and Moderate Deviations for Lossless Streaming Compression of Correlated Sources
We derive upper and lower bounds for the error exponents of lossless streaming compression of two correlated sources under the blockwise and symbolwise settings. We consider the linear scaling regime in which the delay is a scalar multiple of the number of symbol pairs of interest. We show that for rate pairs satisfying certain constraints, the upper and lower bounds for the error exponent of b...
متن کاملExponential bounds on error probability with Feedback
Feedback is useful in memoryless channels for decreasing complexity and increasing reliability; the capacity of the memoryless channels, however, can not be increased by feedback. For fixed length block codes even the decay rate of error probability with block length does not increase with feedback for most channel models. Consequently for making the physical layer more reliable for higher laye...
متن کاملConstructions and bounds on linear error-block codes
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over F2. We also study the asymptotic of linear error-block codes. We define the real valued function αq,m,a(δ), which is an analog of the importa...
متن کاملLower Bounds and Constructions for q - ary Codes Correcting Asymmetric Errors
In this paper, we generalize some lower bounds, constructions and corresponding decoding algorithm from binary codes to the case q-ary codes. We show that some previously known bounds for binary asymmetric error-correcting codes can also be obtained for the generalization.
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 2009