Universal Bounds on the Scaling Behavior of Polar Codes

Abstract

We consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the block error probability, and show that there exists a universal parameter $\mu$ such that for any binary memoryless symmetric channel $W$ with capacity $I(W)$, reliable communication requires rates that satisfy $R<I(W)-\alpha N^{-\frac{1}{\mu }}$, where $\alpha$ is a positive constant and $N$ is the block-length. We provide lower bounds on $\mu$, namely $\mu \ge 3.553$, and we conjecture that indeed $\mu =3.627$, the parameter for the binary erasure channel.

To be presented at ISIT 2012

References in corpus (1)

• Polar Codes: Characterization of Exponent, Bounds, and Constructions

Cited by in corpus (1)

• On Finite-Length Performance of Polar Codes: Stopping Sets, Error Floor, and Concatenated Design