[Paper Review] An interleaver design for polar codes over slow fading channels

Saurabha Tavildar|arXiv (Cornell University)|Oct 16, 2016

Error Correcting Code Techniques8 references3 citations

TL;DR

This paper proposes a diversity interleaver and diversity polar code design to enhance performance over slow fading channels, leveraging bit-reversal mapping of reliable polarized bit channels. The approach achieves near-outage performance (within ~2 dB) and significant gains over random interleavers, especially in block Rayleigh and frequency-hopped OFDM scenarios.

ABSTRACT

We consider the problem of using polar codes over slow fading wireless channels. For design, we focus on a parallel slow fading channel with 2 blocks, and polar codes with rate <= 1/2. Motivated by Arikan's systematic polar code construction, we propose an interleaver design for a general polar code. The interleaver comprises of using the bit reversal of the order of polarized bit channels. This interleaver is called a diversity interleaver. In addition to the diversity interleaver, a diversity polar code is proposed to further increase the diversity gain. The proposed designs are evaluated via link simulations for AWGN and fading channels. The simulation results show a performance close to the outage probability (within 2 dB) and significant gains over using a random interleaver.

Motivation & Objective

• Address the challenge of designing polar codes for slow fading wireless channels where fading distribution varies with deployment and mobility.
• Overcome limitations of existing interleavers (e.g., random, uniform) that fail to maximize diversity gain in block fading environments.
• Develop a universal code design independent of specific fading distributions, focusing on maximizing diversity gain in the worst-case (deep fade) scenario.
• Ensure both code subsets remain self-decodable under successive cancellation decoding, even when one block experiences deep fade.
• Improve performance across diverse wireless scenarios (AWGN, Rayleigh, OFDM) using a single, robust polar code design.

Proposed method

• Propose a diversity interleaver that maps the N/2 most reliable polarized bit channels (set A) and their complement (Aᶜ) using bit-reversal mapping, sending B(A) to block 1 and B(Aᶜ) to block 2.
• Introduce a diversity polar code by constraining the information bit set A such that for every index i, at most one of i or N+1−i is an information bit, satisfying |Aᶜ| = N+1−|A|.
• Use bit-reversal mapping B to ensure symmetry between B(A) and B(Aᶜ), conjecturing that both subsets are self-decodable under successive cancellation decoding.
• Design polar codes via density evolution for BI-AWGN, incorporating the diversity constraint (Equation 1) to maintain performance across fading conditions.
• Evaluate performance across three channel models: AWGN, block Rayleigh fading (2 blocks), and frequency-hopped OFDM with LTE numerology.
• Compare three interleavers: uniform, random, and the proposed diversity interleaver, using BPSK modulation and perfect CSI at the receiver.

Experimental results

Research questions

• RQ1 Can a systematic interleaver design based on bit-reversal mapping of reliable polarized bit channels improve diversity gain in slow fading channels?
• RQ2 Does the proposed diversity interleaver ensure that both subsets (B(A) and B(Aᶜ)) remain self-decodable under successive cancellation decoding?
• RQ3 To what extent does the diversity polar code design, constrained by Equation (1), maintain performance in fading environments compared to standard polar codes?
• RQ4 How does the proposed design compare to random and uniform interleavers in terms of BLER performance over block Rayleigh and OFDM fading channels?
• RQ5 Can the proposed design achieve performance close to the outage probability limit across multiple wireless deployment scenarios?

Key findings

• The diversity polar code with the diversity interleaver achieves performance within ~2 dB of the outage probability limit in block Rayleigh fading channels.
• For N=1024 and N=256, the diversity code with diversity interleaver outperforms both AWGN codes with random and uniform interleavers in Rayleigh fading.
• In AWGN channels, the diversity code performs nearly identically to the standard AWGN-designed polar code, indicating minimal performance loss from the diversity constraint.
• The diversity interleaver provides significant gains over random interleavers in block Rayleigh fading, with performance gains increasing at higher SNR.
• In frequency-hopped OFDM systems (EPA-5, 1x2 MIMO), the diversity interleaver maintains strong performance, though gains are smaller than in block Rayleigh fading.
• The uniform interleaver consistently performs worst across all channel models, confirming the need for structured interleaving in fading environments.