Polar Codes: Speed of Polarization and Polynomial Gap to Capacity
نویسندگان
چکیده
منابع مشابه
extensions of some polynomial inequalities to the polar derivative
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15 صفحه اولChannel Polarization and Polar Codes; Capacity Achieving
A new proposed method for constructing codes that achieves the symmetric capacity (the capacity of the channel with the same probabilities for the inputs), ( ) I W , of any Binary Discrete Memoryless Channel W (B-DMC) will be introduced in this tutorial. This method is based on channel polarization. Channel polarization is the fact that we can synthesize N channels, ( ) { } :1 i N W i N ≤ ≤ , o...
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Shannon’s monumental 1948 work laid the foundations for the rich fields of information and coding theory. The quest for efficient coding schemes to approach Shannon capacity has occupied researchers ever since, with spectacular progress enabling the widespread use of error-correcting codes in practice. Yet the theoretical problem of approaching capacity arbitrarily closely with polynomial compl...
متن کاملPolarization and Polar Codes
This tutorial treats the fundamentals of polarization theory and polar coding. Arıkan’s original results on binary source and channel polarization methods are studied. Error probability and complexity analyses are offered. The original results are generalized in several directions. Early developments in the field are discussed, pointers to some of the important work omitted from this tutorial a...
متن کاملChannel Polarization and Polar Codes
Polar coding is a new technique introduced by Arıkan [1] based on a phenomenon called channel polarization. Polar codes are appealing as an error correction method since they are proved to achieve the symmetric capacity of any B-DMC using low complexity encoders and decoders, and their block error probability is shown to decrease exponentially in the square root of the block length. In fact, tw...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2015
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2014.2371819