DeepAI AI Chat
Log In Sign Up

Decoding Error Probability of the Random Matrix Ensemble over the Erasure Channel

by   Chin Hei Chan, et al.
Nankai University
The Hong Kong University of Science and Technology

Using tools developed in a recent work by Shen and the second author, in this paper we carry out an in-depth study on the average decoding error probability of the random matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random matrix ensemble and the error exponent of the variance, which imply a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.


page 1

page 2

page 3

page 4


A Generalization of the DMC

We consider a generalization of the discrete memoryless channel, in whic...

On Error Decoding of Locally Repairable and Partial MDS Codes

We consider error decoding of locally repairable codes (LRC) and partial...

Error Exponents of Typical Random Codes for the Colored Gaussian Channel

The error exponent of the typical random code is defined as the asymptot...

Successive-Cancellation Decoding of Linear Source Code

This paper investigates the error probability of several decoding method...

A Lower Bound on the Error Exponent of Linear Block Codes over the Erasure Channel

A lower bound on the maximum likelihood (ML) decoding error exponent of ...

A Distance Between Channels: the average error of mismatched channels

Two channels are equivalent if their maximum likelihood (ML) decoders co...