Performance-Complexity-Latency Trade-offs of Concatenated RS-SDBCH Codes

TL;DR

A semi-analytical formula is derived for estimating the decoded frame error rate (FER) at the output of the additive white Gaussian noise channel, obviating the need for time-consuming Monte Carlo simulations.

Abstract

Concatenated bit-interleaved and multilevel coded modulation with outer Reed--Solomon codes, inner Chase-algorithm-based soft-decision-decoded Bose--Ray-Chaudhuri--Hocquenghem codes, and four-level pulse amplitude modulation is considered. A semi-analytical formula is derived for estimating the decoded frame error rate (FER) at the output of the additive white Gaussian noise channel, obviating the need for time-consuming Monte Carlo simulations. The formula is used to search a large space of codes (including the KP4 code) to find those achieving good trade-offs among performance (measured by the gap to the constrained Shannon limit at $10^{-13}$ FER), complexity (measured by the number of elementary decoder operations), and latency (measured by overall block length).

Figures (8)

• Figure 1: Example of an RS-SDBCH concatenation with $M=4$ RS codewords and $m=5$ BCH codewords with the "card-dealing" interleaving scheme. Each square represents one ($B$-bit) RS symbol and the number in each square represents the RS codeword index from which that symbol originates. Here, $K=3$, $N=5$, $k=4B$.
• Figure 2: Example of a BICM codeword with $n=25$, $k=20$ and $B=10$. The shaded and unshaded squares represent the MSBs and LSBs respectively. The rightmost black square is the "zero-pad" LSB paired with one of the parity MSBs.
• Figure 3: Example of an MLC codeword with $n=15$, $k=10$ and $B=10$. The shaded and unshaded squares represent the MSBs and LSBs respectively. The rightmost BCH black square is the "zero-pad" LSB for the rightmost MSB.
• Figure 4: Encoding (top) and decoding (bottom) schemes for MLC with PAM4.
• Figure 5: Decoding scheme of the concatenated system. In the case of MLC, the SDBCH decoder includes the conditional demodulator and demapper as shown in Fig. \ref{['fig:mlc-scheme']}.

Theorems & Definitions (7)

• example 1
• example 2
• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5