Extension of the Poltyrev Bound to Binary Memoryless Symmetric Channels

TL;DR

This paper extends the Poltyrev bound to symmetric channels with discrete outputs, providing tighter error probability bounds and a reduced-complexity version demonstrated on a hybrid BSC-BEC channel.

Contribution

The work generalizes the Poltyrev bound to a broader class of channels and introduces a computationally simpler bound with some loss in accuracy.

Findings

Extended the Poltyrev bound to symmetric channels with discrete outputs

Demonstrated the bound on a hybrid BSC-BEC channel

Introduced a reduced-complexity bound with some loss of tightness

Abstract

The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's weight spectrum. In the present work, the bound is extended to memoryless symmetric channels with a discrete output alphabet. The derived bound is demonstrated on a hybrid BSC-BEC channel. Additionally, a reduced-complexity bound is introduced at the cost of some loss in tightness.