Scaling Exponent of List Decoders with Applications to Polar Codes
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We give a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric channels. The main tool use ...
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Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding arguments, such as ran ...
In the Shannon-theoretic analysis of joint source-channel coding problems, achievability is usually established via a two-stage approach: The sources are compressed into bits, and these bits are reliably communicated across the noisy channels. Random codin ...
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We consider communication over the binary erasure and the binary additive white gaussian noise channels using fixed linear block codes and also appropriate ensembles of such codes. We show concentration of the magnetization over the channel realizations an ...
Polar codes were recently introduced by Arikan. They achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under a low complexity successive cancellation decoding strategy. The original polar code construction is closely rel ...
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Polar codes, introduced recently by Arikan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation, are optimal in th ...
It is shown that given two copies of a q-ary input channel W, where q is prime, it is possible to create two channels W- and W+ whose symmetric capacities satisfy I(W-)
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