# Successive Cancellation List Decoding of Semi-random Unit Memory Convolutional Codes

## TL;DR

This paper introduces a novel successive cancellation list decoding method for semi-random unit memory convolutional codes, improving decoding performance and complexity tradeoffs over traditional methods.

## Contribution

It proposes a new list decoding algorithm using empirical divergence testing for SRUMCCs, with analysis and simulation demonstrating its advantages.

## Key findings

- Outperforms sequential decoding at high SNR
- Achieves performance comparable to polar codes with similar delay
- Provides a closed-form upper bound and simulated lower bound for performance

## Abstract

We present in this paper a special class of unit memory convolutional codes (UMCCs), called semi-random UMCCs (SRUMCCs), where the information block is first encoded by a short block code and then transmitted in a block Markov (random) superposition manner. We propose a successive cancellation list decoding algorithm, by which a list of candidate codewords are generated serially until one passes an empirical divergence test instead of the conventional cyclic redundancy check (CRC). The threshold for testing the correctness of candidate codewords can be learned off-line based on the statistical behavior of the introduced empirical divergence function (EDF). The performance-complexity tradeoff and the performance-delay tradeoff can be achieved by adjusting the statistical threshold and the decoding window size. To analyze the performance, a closed-form upper bound and a simulated lower bound are derived. Simulation results verify our analysis and show that: 1) The proposed list decoding algorithm with empirical divergence test outperforms the sequential decoding in high signal-to-noise ratio (SNR) region; 2) Taking the tail-biting convolutional codes (TBCC) as the basic codes, the proposed list decoding of SRUMCCs have comparable performance with the polar codes under the constraint of equivalent decoding delay.