Sparse Degree Optimization for BATS Codes

TL;DR

This paper explores optimizing the degree distribution in BATS codes to be sparse, improving robustness and computational efficiency while maintaining near-optimal data transmission rates.

Contribution

It introduces methods for achieving sparse degree distributions in BATS codes, balancing computational complexity and performance in various practical scenarios.

Findings

Sparse degree distributions enhance robustness to sampling errors.

Heuristics and exact solutions provide flexible trade-offs.

Sparse distributions maintain near-optimal rates.

Abstract

Batched sparse (BATS) code is a class of batched network code that can achieve a close-to-optimal rate when an optimal degree distribution is provided. We observed that most probability masses in this optimal distribution are very small, i.e., the distribution "looks" sparse. In this paper, we investigate the sparsity optimization of degree distribution for BATS codes that produces sparse degree distributions. There are many advantages to use a sparse degree distribution, say, it is robust to precision errors when sampling the degree distribution during encoding and decoding in practice. We discuss a few heuristics and also a way to obtain an exact sparsity solution. These approaches give a trade-off between computational time and achievable rate, thus give us the flexibility to adopt BATS codes in various scenarios, e.g., device with limited computational power, stable channel condition, etc.