Structured Random Linear Codes (SRLC): Bridging the Gap between Block and Convolutional Codes

TL;DR

This paper introduces Structured Random Linear Codes (SRLC), combining the flexibility of RLC with the efficiency of structured codes to enable practical use in both block and convolutional applications, with optimized signaling.

Contribution

It proposes a new class of codes that integrate structure into RLC, expanding their applicability and efficiency in various coding scenarios, including sliding window convolutional and block modes.

Findings

Enables efficient encoding and decoding for large block sizes.

Supports convolutional and block coding modes with a unified approach.

Provides practical signaling methods for encoder/decoder synchronization.

Abstract

Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a simple yet efficient coding technique, for instance massively used for Network Coding applications. However the price to pay is a high encoding and decoding complexity, especially when working on $GF(2^8)$, which seriously limits the number of packets in the encoding window. On the opposite, structured block codes have been designed for situations where the set of source packets is known in advance, for instance with file transfer applications. Here the encoding and decoding complexity is controlled, even for huge block sizes, thanks to the sparse nature of the code and advanced decoding techniques that exploit this sparseness (e.g., Structured Gaussian Elimination). But their design also prevents their use in convolutional use-cases featuring an encoding window that slides over a continuous set of incoming packets. In this work we try to bridge the gap between these two code classes, bringing some structure to RLC codes in order to enlarge the use-cases where they can be efficiently used: in convolutional mode (as any RLC code), but also in block mode with either tiny, medium or large block sizes. We also demonstrate how to design compact signaling for these codes (for encoder/decoder synchronization), which is an essential practical aspect.