Design of irregular LDPC codes with optimized performance-complexity tradeoff

Abstract

Abstract-The optimal performance-complexity tradeoff for error-correcting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the minimization of decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symmetric channel and any iterative message-passing decoding algorithm with a parallelupdate schedule. A key feature of the proposed optimization method is a new complexity measure that incorporates both the number of operations required to carry out a single decoding iteration and the number of iterations required for convergence. This paper shows that the proposed complexity measure can be accurately estimated from a density-evolution and extrinsicinformation transfer chart analysis of the code. A sufficient condition is presented for convexity of the complexity measure in the variable edge-degree distribution; when it is not satisfied, numerical experiments nevertheless suggest that the local minimum is unique. The results presented herein show that when the decoding complexity is constrained, the complexity-optimized codes significantly outperform threshold-optimized codes at long block lengths, within the ensemble of irregular codes.

Generalized Binary Representation for the Nonbinary LDPC Code With Decoder Design

“…Consider the non-binary LDPC code of rate-half over F 16 in Section V-A. We compare the performance of its GBR with the performance optimized non-binary cycle LDPC codes (optimized under similar assumptions) and the girth optimized binary LDPC codes in the literature.…”

“…The binary computational complexity is only O(q) for BEC. Theoretically, based on the decoding error probability, the authors in [16], [17] prove that the minimal decoding complexities exist if the LDPC codes are constructed with properly chosen degree distributions.…”

Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel

“…For finite number of iterations, a code of non-threshold-optimized distribution may exhibit better convergence property under some specific channel conditions. A performance-complexity tradeoff (PCT) for binary LDPC code over Gaussian channel has been given in [8] where they show that the complexity optimization problem can be reduced to the shaping of the decoding trajectory of EXIT chart for an optimal PCT. However, the global optimal can not be always guaranteed.…”

“…However, the global optimal can not be always guaranteed. Experimental studies show that the local optimal will suffice [8]. One can find more details in [8] for the convex complexity-optimization problem.…”

Irregular Polar Coding for Complexity-Constrained Lightwave Systems

“…C APACITY-approaching forward error correction (FEC) based on low-density parity-check (LDPC) codes [1]- [8] have made a great contribution to increasing data rates of coherent optical transceivers achieving beyond Tb/s [9]- [13]. However, the pursuit of high FEC performance has led to a significant increase in power consumption and circuit size.…”