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

Alvin Y. Sukmadji, Frank R. Kschischang

Abstract

Using a generating function approach, a computationally tractable expression is derived to predict the frame error rate arising at the output of the binary symmetric channel when a number of outer Reed--Solomon codes are concatenated with a number of inner Bose--Ray-Chaudhuri--Hocquenghem codes, thereby obviating the need for time-consuming Monte Carlo simulations. Measuring (a) code performance via the gap to the Shannon limit, (b) decoding complexity via an estimate of the number of operations per decoded bit, and (c) decoding latency by the overall frame length, a code search is performed to determine the Pareto frontier for performance-complexity-latency trade-offs.

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

Abstract

Using a generating function approach, a computationally tractable expression is derived to predict the frame error rate arising at the output of the binary symmetric channel when a number of outer Reed--Solomon codes are concatenated with a number of inner Bose--Ray-Chaudhuri--Hocquenghem codes, thereby obviating the need for time-consuming Monte Carlo simulations. Measuring (a) code performance via the gap to the Shannon limit, (b) decoding complexity via an estimate of the number of operations per decoded bit, and (c) decoding latency by the overall frame length, a code search is performed to determine the Pareto frontier for performance-complexity-latency trade-offs.
Paper Structure (39 sections, 54 equations, 8 figures, 13 tables)

This paper contains 39 sections, 54 equations, 8 figures, 13 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. From Bits to Bytes
  4. Hamming Weight
  5. Generating Functions
  6. Predicting the Frame Error Rate
  7. Miscorrection-Free Analysis
  8. Effects of Miscorrection
  9. Performance-Complexity-Latency Trade-offs
  10. Metrics
  11. Performance
  12. Complexity
  13. Latency
  14. Code Search
  15. Conclusion
  16. ...and 24 more sections

Figures (8)

  • Figure 1: Example of an RS-BCH concatenation with $M=4$ RS codewords and $m=5$ BCH codewords. 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, $K=4$, $N=5$, $k=4B$.
  • Figure 2: Concatenated RS-BCH encoder architecture.
  • Figure 3: Concatenated RS-BCH decoder architecture.
  • Figure 4: FER versus crossover probability for 8 $\times$ RS(544, 514, 15) outer code and 50 $\times$ BCH(940, 880, 6) inner code. We assume that both outer and inner decoders are miscorrection-free.
  • Figure 5: FER versus crossover probability for 8 $\times$ RS(544, 514, 15) outer code and 64 $\times$ BCH(700, 680, 2) inner code with and without miscorrection taken into account. We take miscorrection into account only for received BCH words of error weights 3, 4, and 5.
  • ...and 3 more figures

Theorems & Definitions (7)

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