Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding : (Invited Paper)

Abstract

We propose a binary message passing decoding algorithm for product codes based on generalized minimum distance decoding (GMDD) of the component codes, where the last stage of the GMDD makes a decision based on the Hamming distance metric. The proposed algorithm closes half of the gap between conventional iterative bounded distance decoding (iBDD) and turbo product decoding based on the Chase-Pyndiah algorithm, at the expense of some increase in complexity. Furthermore, the proposed algorithm entails only a limited increase in data flow compared to iBDD.

A novel soft-aided bit-marking decoder for product codes

“…This problem can be solved by re-marking the output bits at each BDD iteration by defining a reliability measure for the outbound BDD decisions. The SR measure proposed in [4,6] linearly combines the BDD decisions with the channels LLRs. We call this new approach SABM-SR.…”

“…A number of new decoding strategies have recently been proposed to tackle both failures and miscorrections, and thus, improve the performance of iBDD decoders whilst preserving an iterative algebraic decoding structure [3][4][5][6][7][8]. Except from [3], all these strategies somehow require the use of soft information from the channel.…”

“…Except from [3], all these strategies somehow require the use of soft information from the channel. For instance in [4,6], the channel bit reliabilities are updated at each iteration based on the previous BDD output and are used to produce new hard decisions for the next BDD decoding stage.…”

“…In this contribution, we extend the SABM algorithm to include scaled reliabilities (SRs) in the decoding process. Differently from [4,6], the SRs are used to update the bit-marking process at each decoding iteration. The proposed design efficiently merges SABM and SRs to optimise the decoding of PCs.…”

Improved Decoding of Staircase Codes: The Soft-Aided Bit-Marking (SABM) Algorithm

“…The algorithm of [16] outperforms [14], but it suffers from an increased complexity as anchor codewords need to be tracked during iterative BDD. Very recently, a modified iterative BDD for PCs was proposed in [17]- [20]. In this algorithm, channel reliabilities are used to perform the final HD at the output of BDD, instead of directly accepting the decoding result.…”