Abstract
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. Deviating from Shannon’s 1959 solid angle argument, we project the problem into two dimensions and apply standard trigonometry. This enables us to also analyze Gaussian random codes in additive white Gaussian noise and binary random codes for the binary symmetric channel. We find that the Voronoi regions harden doubly-exponential in the blocklength and utilize that to propose the new median bound that outperforms Shannon’s 1959 sphere packing bound for the uniform spherical ensemble, whenever the code contains more than three codewords. Furthermore, we propose a very tight approximation to simplify computation of both exact error probability and the two bounds.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
