DeepAI AI Chat
Log In Sign Up

Polar Codes' Simplicity, Random Codes' Durability

by   Hsin-Po Wang, et al.

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 ς-ary 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.


Complexity and Second Moment of the Mathematical Theory of Communication

The performance of an error correcting code is evaluated by its error pr...

Log-logarithmic Time Pruned Polar Coding

A pruned variant of polar coding is proposed for binary erasure channels...

Polar-like Codes and Asymptotic Tradeoff among Block Length, Code Rate, and Error Probability

A general framework is proposed that includes polar codes over arbitrary...

Concatenated Classic and Neural (CCN) Codes: ConcatenatedAE

Small neural networks (NNs) used for error correction were shown to impr...

Polar Coded Repetition for Low-Capacity Channels

Constructing efficient low-rate error-correcting codes with low-complexi...

Polar Codes for Quantum Reading

Quantum reading provides a general framework where to formulate the stat...

Physical layer insecurity

In the classic wiretap model, Alice wishes to reliably communicate to Bo...