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Asilomar Conference on Signals, Systems and Computers (ACSSC)

Decoder diversity architectures for finite alphabet iterative decoders

Bane V. Vasic, David Declercq, Shiva Kumar Planjery

Published Nov 1, 2014• 1 citation
Publisher

Abstract

We present a finite alphabet iterative decoders (FAIDs), a new type of decoders for low-density parity check (LDPC) codes, which outperform much more complex belief-propagation-based counterparts in the error floor region. The FAID variable node update is a simple Boolean map, and we show that by varying this map one can achieve a class of decoders capable of correcting wide range of distinct error patterns uncorrectable by a single FAID. We call this concept decoding diversity, and present a low-complexity architecture and error performance analysis of the FAID diversity decoder for column-weight three LDPC codes on the binary symmetric channel.

DOI
10.1109/acssc.2014.7094412

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We present a finite alphabet iterative decoders (FAIDs), a new type of decoders for low-density parity check (LDPC) codes, which outperform much more complex belief-propagation-based counterparts in the error floor region. The FAID variable node update is a simple Boolean map, and we show that by varying this map one can achieve a class of decoders capable of correcting wide range of distinct error patterns uncorrectable by a single FAID. We call this concept decoding diversity, and present a low-complexity architecture and error performance analysis of the FAID diversity decoder for column-weight three LDPC codes on the binary symmetric channel.
Recently, we introduced a new class of finite alphabet iterative decoders (FAIDs) for low-density parity-check (LDPC) codes. These decoders are capable of surpassing belief propagation (BP) in the error floor region on the binary symmetric channel (BSC) with much lower complexity. In this paper, we introduce a novel scheme with the objective of guaranteeing the correction of a given and potentially large number of errors on column-weight-three LDPC codes. The proposed scheme uses a plurality of FAIDs which collectively correct more error patterns than a single FAID on a given code. The collection of FAIDs utilized by the scheme is judiciously chosen to ensure that individual decoders have different decoding dynamics and correct different error patterns. Consequently, they can collectively correct a diverse set of error patterns, which is referred to as decoder diversity. We provide a systematic method to generate the set of FAIDs for decoder diversity on a given code based on the knowledge of the most harmful trapping sets present in the code. Using the well-known column-weight-three (155,64) Tanner code with dmin= 20 as an example, we describe the method in detail and show, by means of exhaustive simulation, that the guaranteed error correction capability on short length LDPC codes can be significantly increased with decoder diversity.
Low-density parity-check (LDPC) codes are adopted in many applications due to their Shannon-limit approaching error-correcting performance. Nevertheless, belief-propagation (BP) based decoding of these codes suffers from the error-floor problem. Recently, a new type of decoders termed finite alphabet iterative decoders (FAIDs) were introduced. The FAIDs use simple Boolean maps for variable node processing. With very short word length, they can surpass the BP-based decoders in the error floor region. This paper develops a low-complexity implementation architecture for FAIDs by making use of their properties. Particularly, an innovative bit-serial check node unit is designed for FAIDs, and the symmetric Boolean maps for variable node processing lead to small silicon area. An optimized data scheduling scheme is also proposed to increase the hardware utilization efficiency. From synthesis results, the proposed FAID implementation needs only 52% area to reach the same throughput as one of the most efficient Min-sum decoders for an example (7807, 7177) LDPC code, while achieving better error-correcting performance in the error-floor region.
Low-density parity-check (LDPC) codes are adopted in many applications due to their Shannon-limit approaching error-correcting performance. Nevertheless, belief-propagation (BP) based decoding of these codes suffers from the error-floor problem, i.e., an abrupt change in the slope of the error-rate curve that occurs at very low error rates. Recently, a new type of decoders termed finite alphabet iterative decoders (FAIDs) were introduced. The FAIDs use simple Boolean maps for variable node processing, and can surpass the BP-based decoders in the error floor region with very short word length. We restrict the scope of this paper to regular dv=3 LDPC codes on the BSC channel. This paper develops a low-complexity implementation architecture for the FAIDs by making use of their properties. Particularly, an innovative bit-serial check node unit is designed for the FAIDs, and a small-area variable node unit is proposed by exploiting the symmetry in the Boolean maps. Moreover, an optimized data scheduling scheme is proposed to increase the hardware utilization efficiency. From synthesis results, the proposed FAID implementation needs only 52% area to reach the same throughput as one of the most efficient standard Min-Sum decoders for an example (7807, 7177) LDPC code, while achieving better error-correcting performance in the error-floor region. Compared to an offset Min-Sum decoder with longer word length, the proposed design can achieve higher throughput with 45% area, and still leads to possible performance improvement in the error-floor region.
Decoder diversity is a powerful error correction framework in which a collection of decoders collaboratively correct a set of error patterns otherwise uncorrectable by any individual decoder. In this paper, we propose a new approach to design the decoder diversity of finite alphabet iterative decoders (FAIDs) for Low-Density Parity Check (LDPC) codes over the binary symmetric channel (BSC), for the purpose of lowering the error floor while guaranteeing the waterfall performance. The proposed decoder diversity is achieved by training a recurrent quantized neural network (RQNN) to learn/design FAIDs. We demonstrated for the first time that a machine-learned decoder can surpass in performance a man-made decoder of the same complexity. As RQNNs can model a broad class of FAIDs, they are capable of learning an arbitrary FAID. To provide sufficient knowledge of the error floor to the RQNN, the training sets are constructed by sampling from the set of most problematic error patterns - trapping sets. In contrast to the existing methods that use the cross-entropy function as the loss function, we introduce a frame-error-rate (FER) based loss function to train the RQNN with the objective of correcting specific error patterns rather than reducing the bit error rate (BER). The examples and simulation results show that the RQNN-aided decoder diversity increases the error correction capability of LDPC codes and lowers the error floor.
Decoder diversity is a powerful error correction framework in which a collection of decoders collaboratively correct a set of error patterns otherwise uncorrectable by any individual decoder. In this paper, we propose a new approach to design the decoder diversity of finite alphabet iterative decoders (FAIDs) for Low-Density Parity Check (LDPC) codes over the binary symmetric channel (BSC), for the purpose of lowering the error floor while guaranteeing the waterfall performance. The proposed decoder diversity is achieved by training a recurrent quantized neural network (RQNN) to learn/design FAIDs. We demonstrated for the first time that a machine-learned decoder can surpass in performance a man-made decoder of the same complexity. As RQNNs can model a broad class of FAIDs, they are capable of learning an arbitrary FAID. To provide sufficient knowledge of the error floor to the RQNN, the training sets are constructed by sampling from the set of most problematic error patterns - trapping sets. In contrast to the existing methods that use the cross-entropy function as the loss function, we introduce a frame-error-rate (FER) based loss function to train the RQNN with the objective of correcting specific error patterns rather than reducing the bit error rate (BER). The examples and simulation results show that the RQNN-aided decoder diversity increases the error correction capability of LDPC codes and lowers the error floor.
We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the binary symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are quantized versions of the belief propagation (BP) decoder, the proposed finite alphabet iterative decoders (FAIDs) do not propagate quantized probabilities or log-likelihoods and the variable node update functions do not mimic the BP decoder. Rather, the update functions are maps designed using the knowledge of potentially harmful subgraphs that could be present in a given code, thereby rendering these decoders capable of outperforming the BP in the error floor region. On certain column-weight-three codes of practical interest, we show that there exist {FAIDs that surpass the floating-point BP decoder in the error floor region while requiring only three bits of precision for the representation of the messages}. Hence, FAIDs are able to achieve a superior performance at much lower complexity. We also provide a methodology for the selection of FAIDs that is not code-specific, but gives a set of candidate FAIDs containing potentially good decoders in the error floor region for any column-weight-three code. We validate the code generality of our methodology by providing particularly good three-bit precision FAIDs for a variety of codes with different rates and lengths.