The lowest-possible BER and FER for any discrete memoryless channel with given capacity

TL;DR

This paper explores the fundamental limits of channel coding for discrete memoryless channels, focusing on minimizing frame error ratio at rates above capacity, revealing a contradiction with minimizing bit error ratio.

Contribution

It introduces a novel analysis of coding schemes optimized for lowest frame error ratio, contrasting with traditional schemes aimed at minimizing bit errors.

Findings

Minimum-possible FER is achieved by a different coding scheme than minimum BER.

Optimizing for FER and BER leads to conflicting coding strategies.

Application of results demonstrates practical implications for channel coding design.

Abstract

We investigate properties of a channel coding scheme leading to the minimum-possible frame error ratio when transmitting over a memoryless channel with rate R>C. The results are compared to the well-known properties of a channel coding scheme leading to minimum bit error ratio. It is concluded that these two optimization requests are contradicting. A valuable application of the derived results is presented.