Successive Cancellation Decoding of Single Parity-Check Product Codes

TL;DR

This paper proposes a successive cancellation decoding method for single parity-check product codes, deriving recursive formulas, analyzing error probabilities over erasure channels, and demonstrating improved performance over Elias' original decoding.

Contribution

It introduces a novel SC decoding algorithm for SPC-PCs, with recursive formulas and error analysis, improving upon Elias' classical decoding approach.

Findings

SC decoding achieves lower block error probability than Elias' decoding

Recursive formulas for SC decoding of SPC-PCs are derived

Error probability bounds are established and compared

Abstract

We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding.