On GRAND-Assisted Vector Random Linear Network Coding in Wireless Broadcasts.

Area of Science:

• Information Theory
• Coding Theory
• Wireless Communications

Background:

• Existing random linear network coding (RLNC) schemes are limited to scalar operations over GF(2L).
• Combining RLNC with guessing random additive noise decoding (GRAND) aids error correction before decoding, reducing packet loss in wireless broadcast networks.

Purpose of the Study:

• To generalize the GRAND-assisted decoding framework for vector RLNC over GF(2)L.
• To propose a design rule for vector RLNC enabling efficient error vector estimation without extra computation.
• To characterize conditions for the correctness of estimated error vectors.

Main Methods:

• Formulation of a general GRAND-assisted decoding framework for vector RLNC.
• Development of a design rule for vector RLNC schemes.
• Construction of two explicit vector RLNC schemes based on the proposed rule.
• Analytical evaluation of performance and complexity.

Main Results:

• The first vector RLNC scheme, based on matrix representation, matches scalar RLNC completion delay while reducing computational complexity by up to 37.3%.
• The second vector RLNC scheme, using sparse coding, further decreases computational complexity by up to 33.6% compared to the first scheme, with a minor impact on delay.
• Necessary and sufficient conditions for the correctness of efficiently obtained estimated error vectors were established.

Conclusions:

• Vector RLNC with GRAND offers a more computationally efficient approach for wireless broadcast networks.
• The proposed design rule facilitates the development of practical and efficient vector RLNC schemes.
• These advancements contribute to reducing packet erasure rates and improving network performance.