[Paper Review] Fast Simplified Successive-Cancellation List Decoding of Polar Codes

Seyyed Ali Hashemi, Carlo Condo+1 more|arXiv (Cornell University)|Jan 27, 2017

Error Correcting Code Techniques8 references4 citations

TL;DR

This paper proposes Fast-SSCL, a novel decoding algorithm for polar codes that accelerates the decoding of Rate-1 nodes by reducing the number of required bit estimations to min(L−1, Nν), where L is the list size and Nν is the node length. By replacing the standard Rate-1 decoder in SSCL with this optimized version, Fast-SSCL achieves up to 66.6% fewer time-steps than SSCL and 88.1% fewer than SCL, with no loss in error-correction performance.

ABSTRACT

Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time-steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.

Motivation & Objective

• To reduce the latency of successive-cancellation list (SCL) decoding for polar codes without sacrificing error-correction performance.
• To address the inefficiency of existing Rate-1 node decoders in SSCL and SCL, which require full-length processing regardless of list size.
• To develop a minimal, exact decoding method for Rate-1 nodes that matches SCL/SSCL performance using only min(L−1, Nν) bit estimations.
• To demonstrate significant time-step reduction in practical polar code decoding by exploiting the structure of Rate-1 nodes.

Proposed method

• Proposes a new decoding strategy for Rate-1 nodes that requires only min(L−1, Nν) bit estimations to match SCL and SSCL performance.
• Replaces the standard Rate-1 decoder in SSCL with a faster, minimal estimator that avoids redundant computations.
• Uses a theoretical proof to show that estimating only the L−1 least reliable bits (or all Nν if L−1 ≥ Nν) is sufficient for exact performance matching.
• Integrates the new Rate-1 decoder into the SSCL framework to create Fast-SSCL, preserving the original algorithm’s error-correction guarantees.
• Employs a hardware-friendly formulation of LLR operations to maintain efficiency in practical implementations.
• Validates the method through case studies on polar codes of length N=1024 with varying rates and list sizes.

Experimental results

Research questions

• RQ1 Can the number of bit estimations in Rate-1 node decoding be reduced below the full length Nν without performance loss?
• RQ2 Is it possible to achieve the same error-correction performance as SCL and SSCL using only min(L−1, Nν) estimations in Rate-1 nodes?
• RQ3 Does the proposed method yield significant time-step reduction in polar code decoding across different code rates and list sizes?
• RQ4 Can the new decoder be integrated into SSCL without altering its performance guarantees?
• RQ5 What is the maximum achievable reduction in decoding time-steps for practical polar codes using this approach?

Key findings

• Fast-SSCL reduces the number of decoding time-steps by up to 66.6% compared to SSCL and 88.1% compared to SCL for polar codes with high rates and large list sizes.
• For a P(1024, 860) code with L=128, the empirical method in [7] causes a 0.25 dB performance loss at FER=10−5, while Fast-SSCL maintains exact performance.
• The proposed Rate-1 node decoder requires only min(L−1, Nν) bit estimations, which is significantly fewer than the Nν steps in SSCL and 3Nν−2 in SCL.
• At rate 3/4 and L=2, Fast-SSCL achieves 66.6% fewer time-steps than SSCL and 88.1% fewer than SCL.
• The time-step reduction is most pronounced at high code rates, where Rate-1 nodes are more numerous and longer in length.
• The method is universally applicable to any polar code and does not require code-specific redesign or approximations.