VLSI Implementation of a Rate Decoder for Structural LDPC Channel Codes

AbstractThis paper proposes a low complexity low-density parity check decoder (LDPC) design. The design mainly accomplishes a message passing algorithm and systolic high throughput architecture. The typical mathematical calculations are based on the observation that nodes with high log likelihood ratio provide almost same information in every iteration and can be considered as stationary, we propose an algorithm in which the parity check matrix H is updated to a reduced complexity form every time a stationary node is encountered which results in lesser number of numerical computations in subsequent iterations. In this paper, we contemplately focuses on computational complexity and the decoder design significantly benefits from the high throughput point of view and the various improvisations introduced at various levels of abstraction in the decoder design. Threshold Controlled Min Sum Algorithm implements the LDPC decoder design for a code compliant with wired and wireless applications. A high performance LDPC decoder has been designed that achieves a throughput of 0.890 Gbps. The whole design of LDPC Decoder is designed, simulated and synthesized using Xilinx ISE 13.1 EDA Tool

Relaxed Half-Stochastic Belief Propagation

Low-density parity-check codes are attractive for high throughput applications because of their low decoding complexity per bit, but also because all the codeword bits can be decoded in parallel. However, achieving this in a circuit implementation is complicated by the number of wires required to exchange messages between processing nodes. Decoding algorithms that exchange binary messages are interesting for fully-parallel implementations because they can reduce the number and the length of the wires, and increase logic density. This paper introduces the Relaxed Half-Stochastic (RHS) decoding algorithm, a binary message belief propagation (BP) algorithm that achieves a coding gain comparable to the best known BP algorithms that use real-valued messages. We derive the RHS algorithm by starting from the well-known Sum-Product algorithm, and then derive a low-complexity version suitable for circuit implementation. We present extensive simulation results on two standardized codes having different rates and constructions, including low bit error rate results. These simulations show that RHS can be an advantageous replacement for the existing state-of-the-art decoding algorithms when targeting fully-parallel implementations

On a Different Perspective and Approach to Implement Adaptive Normalized BP-based Decoding for LDPC Codes

In this paper, we propose an improved version of the min-sum algorithm for low density parity check (LDPC) code decoding, which we call “adaptive normalized BP-based” algorithm. Our decoder provides a compromise solution between the belief propagation and the min-sum algorithms by adding an exponent offset to each variable node’s intrinsic information in the check node update equation. The extrinsic information from the min-sum decoder is then adjusted by applying a negative power of two scale factor, which can be easily implemented by right shifting the min-sum extrinsic information. The difference between our approach and other adaptive normalized min-sum decoders is that we select the normalization scale factor using a clear analytical approach based on underlying principles. Simulation results show that the proposed decoder outperforms the min-sum decoder and performs very close to the BP decoder, but with lower complexity.Keywords: modified min-sum, belief propagation, sum product, min-sum, LDPC codes, iterative decodin

On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes

The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly out-perform, the ideal belief-propagation algorithm at observed error rates