# Successive-Cancellation Decoding of Linear Source Code

## TL;DR

This paper analyzes the error probabilities of various decoding methods for source codes with side information, demonstrating the effectiveness of successive-cancellation decoding and its stochastic variant for polar source codes.

## Contribution

It establishes the effectiveness of successive-cancellation and stochastic successive-cancellation decoding methods for source codes, including polar codes, in the asymptotic error probability sense.

## Key findings

- Successive-cancellation decoding is effective for source codes with side information.
- Stochastic successive-cancellation decoding is also effective for polar source codes.
- Error probability approaches zero as code length increases.

## Abstract

This paper investigates the error probability of several decoding methods for a source code with decoder side information, where the decoding methods are: 1) symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding, and 3) stochastic successive-cancellation decoding. The proof of the effectiveness of a decoding method is reduced to that for an arbitrary decoding method, where `effective' means that the error probability goes to zero as $n$ goes to infinity. Furthermore, we revisit the polar source code showing that stochastic successive-cancellation decoding, as well as successive-cancellation decoding, is effective for this code.