Low-complexity Finite-Precision Decoders for LDPC Codes

Zeina Mheich, Truong Nguyen, Valentin Savin +1 more

Classically, the quantization of the soft information supplied to a finite-precision decoder is chosen to optimize a certain criterion which does not depend on the characteristics of the existing code. This work studies code-aware quantizers, for finite-precision min-sum decoders, which optimize the noise threshold of the existing family of Low-Density Parity-Check (LDPC) codes. We propose a code-aware quantizer with lower complexity than that obtained by optimizing all decision levels and approaching its performance, for few quantization bits. We show that code-aware quantizers outperform code-independent quantizers in terms of noise threshold for both regular and irregular LDPC codes. To overcome the error floor behavior of LDPC codes, we propose the design of the quantizer for a target error probability at the decoder output. The results show that the quantizer optimized to get a zero error probability could lead to a very bad performance for practical range of signal to noise ratios. Finally, we propose to design jointly irregular LDPC codes and code-aware quantizers for finite-precision min-sum decoders. We show that they achieve significant decoding gains with respect to LDPC codes designed for infinite-precision belief propagation decoding, but decoded by finite-precision min-sum.

Amrit Pal Singh, Sanjay Sharma

Toshiaki Koike–Akino, David S. Millar, Keisuke Kojima +4 more

Recent low-density parity-check (LDPC) codes have shown capacity-approaching performance for various communications systems. However, their promising performance cannot always be obtained due to practical constraints, such as finite codeword length, finite iteration, finite memory, and finite precision. In this paper, we focus on a practical design method of high-performance LDPC codes under a constraint of finite-iteration decoding for low-power optical communications. We introduce an iteration-aware LDPC code design approach, which is based on decoding trajectory in extrinsic information transfer chart analysis. It is demonstrated that an LDPC code designed by the conventional curve-fitting method exhibits nearly 2 dB of penalty, when the maximum number of iterations is limited. The results suggest that the LDPC code should be adaptively changed, e.g., when the number of decoding iterations is decreased to save power consumption. We also extend our design method to a multi-objective optimization concept by taking average degrees into account, so that the threshold and the computational complexity are minimized at the same time. The proposed Pareto-optimal codes can achieve additional 2-dB gain or 50% complexity reduction at maximum, in low-power decoding scenarios.

Massimo Rovini, Guido Masera, Luca Fanucci +4 more

Massimo Rovini, Luca Fanucci, Francesco Rossi

Maximilian Stark, Gerhard Bauch, Linfang Wang +1 more

The new 5G communications standard increases data rates and supports low-latency communication that places constraints on the computational complexity of channel decoders. 5G low-density parity-check (LDPC) codes have the so-called protograph-based raptor-like (PBRL) structure which offers inherent rate-compatibility and excellent performance. Practical LDPC decoder implementations use message-passing decoding with finite precision, which becomes coarse as complexity is more severely constrained. Performance degrades as the precision becomes more coarse. Recently, the information bottleneck (IB) method was used to design mutual-information-maximizing lookup tables that replace conventional finite-precision node computations. The IB approach exchanges messages represented by integers with very small bit width. This paper extends the IB principle to the flexible class of PBRL LDPC codes as standardized in 5G. The extensions include puncturing and rate-compatible IB decoder design. As an example of the new approach, a 4-bit information bottleneck decoder is evaluated for PBRL LDPC codes over a typical range of rates. Frame error rate simulations show that the proposed scheme outperforms offset min-sum decoding algorithms and operates very close to double-precision sum-product belief propagation decoding.