2012/05/13 by Ali Goli, Goli, Ali, S. Hamed Hassani +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1205.2876
To be presented at ISIT 2012
arxiv created 2012/05/13 · openalex publication_date 2012/05/13 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 μ such that for any binary memoryless symmetric channel W with capacity I(W), reliable communication requires rates that satisfy R< I(W)-αN^-\frac1μ, where α is a positive constant and N is the block-length. We provide lower bounds on μ, namely μ≥ 3.553, and we conjecture that indeed μ=3.627, the parameter for the binary erasure channel.