Approaching Maximum Likelihood Decoding Performance via Reshuffling Ordered Reliability Bits Guessing Random Additive Noise Decoding (RS-ORBGRAND)

Core Concepts

A new variant of Ordered Reliability Bits Guessing Random Additive Noise Decoding (ORBGRAND), termed RS-ORBGRAND, is proposed to approach the performance of Maximum Likelihood (ML) decoding while retaining the hardware-friendly properties of ORBGRAND.

Abstract

The paper proposes a new decoding scheme called RS-ORBGRAND, which is an improvement over the existing ORBGRAND decoder. ORBGRAND is a variant of the Guessing Random Additive Noise Decoding (GRAND) framework that is particularly suitable for short and high-rate block codes, as it can be efficiently implemented in hardware.

The key idea behind RS-ORBGRAND is to reshuffle the querying order of ORBGRAND to better approximate the optimal Maximum Likelihood (ML) decoding performance. The authors analyze an idealized "search problem" to derive insights on the optimal querying order, which should have a monotonically non-increasing sequence of expected probabilities of finding the correct codeword.

Based on this analysis, RS-ORBGRAND first uses an existing ORBGRAND scheme to obtain the expected probability sequence, and then reshuffles the queries to sort this sequence in descending order. This reshuffling step is performed offline, so the decoding process itself still maintains the hardware-friendly properties of ORBGRAND.

Numerical simulations on BCH and polar codes show that RS-ORBGRAND can achieve a gain of at least 0.3dB over existing ORBGRAND variants, and is only 0.1dB away from the ML decoding lower bound, at block error rates as low as 10^-6. The authors also demonstrate the importance of using a sufficiently large set of candidate error patterns in the reshuffling step to achieve this performance.

Stats

For BCH(127, 113) code at 4dB, the average number of queries for ORBGRAND is 790.8, while for RS-ORBGRAND it is 715.6.
For BCH(127, 113) code at 7dB, the average number of queries for ORBGRAND is 1.479, while for RS-ORBGRAND it is 1.350.
For CRC-aided Polar(128, 114) code at 6.8dB, the block error rate for RS-ORBGRAND with T1=5e4 is around 10^-6, which is only 0.1dB away from the ML decoding lower bound.

Quotes

"Numerical simulations show that RS-ORBGRAND leads to noticeable gains compared with ORBGRAND and its existing variants, and is only 0.1dB away from ML decoding, for BLER as low as 10−6."
"Using a sufficiently large set of candidate error patterns is crucial for achieving good performance with RS-ORBGRAND."

Key Insights Distilled From

Approaching Maximum Likelihood Decoding Performance via Reshuffling ORBGRAND

by Li Wan,Wenyi... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2401.15946.pdf

Deeper Inquiries

How can the insights from the idealized "search problem" analysis be further leveraged to design even more efficient decoding schemes?

The insights gained from the idealized "search problem" analysis can be further leveraged to design more efficient decoding schemes by focusing on optimizing the querying process. By understanding the expected number of queries and the monotonicity property required for efficient decoding, designers can develop new ordering policies that minimize the querying complexity while maximizing decoding performance. Additionally, leveraging the reshuffling technique based on the monotonicity property can lead to improved decoding schemes that approach the performance of ML decoding. By incorporating these insights into the design of decoding algorithms, researchers can enhance the efficiency and effectiveness of decoding processes for various codes and channel models.

What are the potential challenges in extending the RS-ORBGRAND approach to other channel models or code families beyond short block codes?

Extending the RS-ORBGRAND approach to other channel models or code families beyond short block codes may pose several challenges. One challenge is the complexity of adapting the reshuffling technique to different channel models with varying noise characteristics. Different channel models may require specific adjustments to the reshuffling process to ensure optimal performance. Additionally, applying the RS-ORBGRAND approach to code families with different structures and properties could require significant modifications to accommodate diverse coding schemes. Ensuring the effectiveness and efficiency of the reshuffling technique across a wide range of channel models and code families may require extensive testing and optimization.

Can the reshuffling technique be combined with other GRAND variants or decoding algorithms to achieve even closer performance to ML decoding?

Yes, the reshuffling technique can be combined with other GRAND variants or decoding algorithms to achieve even closer performance to ML decoding. By integrating the reshuffling technique with existing GRAND variants that utilize different heuristics or metrics for querying, researchers can potentially enhance the overall decoding performance. For example, combining the reshuffling technique with list decoding or adaptive querying strategies could further improve the efficiency and accuracy of the decoding process. By leveraging the strengths of different decoding algorithms and incorporating the reshuffling approach, it is possible to develop decoding schemes that approach or even match the performance of ML decoding across a wide range of codes and channel models.