Concatenated Forward Error Correction With KP4 and Single Parity Check Codes

Concatenated forward error correction is studied using an outer KP4 Reed-Solomon code with hard-decision decoding and inner single parity check (SPC) codes with Chase/Wagner soft-decision decoding. Analytical expressions are derived for the end-to-end frame and bit error rates for transmission over additive white Gaussian noise channels with binary phase-shift keying (BPSK) and quaternary amplitude shift keying (4-ASK), as well as with symbol interleavers and quantized channel outputs. The BPSK error rates are compared to those of two other inner codes: a two-dimensional product code with SPC component codes and an extended Hamming code. Simulation results for unit-memory inter-symbol interference channels and 4-ASK are also presented. The results show that the coding schemes achieve similar error rates, but SPC codes have the lowest complexity and permit flexible rate adaptation.

I. Introduction

Applications such as data center networks (DCNs) and data center interconnects (DCIs) over short-reach fiber optic links have high throughput and strict latency constraints. Next-generation Ethernet standards should provide data rates of to [1], [2] while guaranteeing bit error rates (BERs) below and latencies below [3], [4]. Forward error correction (FEC) is essential to meet these requirements, and current systems rely on the KP4 code [5], which is a (544,514) Reed-Solomon (RS) code over with the rate and overhead (OH) .