
Complexity and Second Moment of the Mathematical Theory of Communication
The performance of an error correcting code is evaluated by its error pr...
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Loglogarithmic Time Pruned Polar Coding
A pruned variant of polar coding is proposed for binary erasure channels...
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Polarlike Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability
A general framework is proposed that includes polar codes over arbitrary...
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On Approximation, Bounding Exact Calculation of Block Error Probability for Random Codes
This paper presents a method to calculate the exact block error probabil...
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LDPC Codes with Local and Global Decoding
This paper presents a theoretical study of a new type of LDPC codes that...
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Universal codes in the sharedrandomness model for channels with general distortion capabilities
We put forth new models for universal channel coding. Unlike standard co...
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On Universal Codes for Integers: Wallace Tree, Elias Omega and Variations
A universal code for the (positive) integers can be used to store or com...
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Polar Codes' Simplicity, Random Codes' Durability
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively, for any constants π,ρ>0 such that π+2ρ<1, we construct a sequence of error correction codes with block length N approaching infinity, block error probability (N^π), code rate N^ρ less than the Shannon capacity, and encoding and decoding complexity O(Nlog N) per code block. The putative codes take uniform ςary messages for sender's choice of prime ς. The putative codes are optimal in the following manner: Should π+2ρ>1, no such codes exist for generic channels regardless of alphabet and complexity.
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