Fano Decoder Research Articles

On the improvements of successive cancellation Creeper decoding for polar codes

In this paper, an improvement for successive cancellation (SC) decoding is presented for polar codes. This improvement is based on applying Creeper approach that was used to decode convolutional codes. The proposed decoder combines a stack and a Fano approaches, allowing to significantly decrease complexity of Successive Cancellation Fano decoder at the cost of a slight increase in space complexity. We also show how to combine the SC-Creeper decoding with a bit-flipping approach to further improve the performance of SC-Creeper due to introducing additional decoding attempts.Simulation results show that the proposed SC-Creeper and SC-Creeper Flip decoders with carefully selected parameters have the same performance as both CRC-aided Successive Cancellation List decoder with list size 8 and Fano decoder, while having much smaller complexity.

Hardware Implementation of Fano Decoder for Polarization-Adjusted Convolutional (PAC) Codes

This brief proposes a hardware implementation architecture for Fano decoding of polarization-adjusted convolutional (PAC) codes. This architecture uses a novel branch metric unit specific to PAC codes. The proposed decoder is tested on FPGA, and its performance is evaluated on ASIC using TSMC 28 nm 0.72 V library. The decoder can be clocked at 500 MHz and reach an average information throughput of 38 Mb/s at 3.5 dB signal-to-noise ratio for a block length of 128 and a code rate of 1/2.

Polarization-Adjusted Convolutional (PAC) Codes: Sequential Decoding vs List Decoding

In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Arikan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this concatenation are called polarization-adjusted convolutional (PAC) codes . In this scheme, a pair of polar mapper and demapper as pre- and post- processing devices are deployed around a memoryless channel, which provides polarized information to an outer decoder leading to improved error correction performance of the outer code. In this paper, the list decoding and sequential decoding (including Fano decoding and stack decoding) are first adapted for use to decode PAC codes. Then, to reduce the complexity of sequential decoding of PAC/polar codes, we propose (i) an adaptive heuristic metric, (ii) tree search constraints for backtracking to avoid exploration of unlikely sub-paths, and (iii) tree search strategies consistent with the pattern of error occurrence in polar codes. These contribute to the reduction of the average decoding time complexity from 50% to 80%, trading with 0.05 to 0.3 dB degradation in error correction performance within FER = $10^{-3}$ range, respectively, relative to not applying the corresponding search strategies. Additionally, as an important ingredient in Fano decoding of PAC/polar codes, an efficient computation method for the intermediate LLRs and partial sums is provided. This method is effective in backtracking and avoids storing the intermediate information or restarting the decoding process. Eventually, all three decoding algorithms are compared in terms of performance, complexity, and resource requirements.

High throughput graphics processing unit based Fano decoder

The next-generation high speed wireless technologies, such as WirelessHD, bring the concept of several Gigabits per second data communication. However, forward error correction that takes place at the receiver side has become a real computational challenge. So far, only hardware solutions have offered such high-speed convolutional decoding, which could not be achieved by software solutions. Our paper aims to fill this gap and proposes a software level solution offering such multi-Gbps convolutional decoding. For this intend, we use the massively parallel computing power of NVIDIA GPGPUs and CUDA programming environment to implement a solution. As a decoding method, the Fano algorithm is selected for its relatively low memory requirements and computational complexity. A look-ahead mechanism and compact history in the form of circular queue is presented to support such high throughput. Conducted tests showed that our GPU based algorithm can decode up to 9.25Gbps.

Fast and upper bounded Fano decoding algorithm: queuing analysis

AbstractIn computer networking, having limited buffer size is one of the vital causes of splitting the messages into smaller frames to be then transmitted over the network. Increasing the buffer size will not improve the case much but rather it is likely to degrade the performance of the system if it is not investigated properly. On the other hand, frames' retransmissions, as a result of frames being corrupted or dropped, need to be avoided as much as possible because of possible network congestion. To investigate the problem of undesired retransmissions, this paper addresses the use of convolutional codes utilising variable complexity decoding algorithms, such as the Fano algorithm, which mainly aim to mitigate frames' retransmissions caused by frames' corruption. It is noteworthy to mention that the rapid growth of wireless technologies has attracted everybody's attention. As wireless technology evolves, new decoding algorithms are emerging to demonstrate designs with variable power consumptions. Hence, in this paper, we propose a novel queuing model that describes not only frame arriving and departing processes after getting decoded according to how worse the channel condition is or what is the remaining system power but also a decoder with a double speed compared with what is best scrutinised in the literature. Moreover, in our buffering model, we can reduce the number of frames being dropped because of insufficient buffer size, and unwanted retransmissions owing to long frame waiting time, by virtue of bestowing larger buffer size, through our derived closed‐form expression that represents the expected number of awaiting frames in the buffers of Fano decoders parameterised by channel status, decoding threshold and frame arriving probability. As far as the system occupancy is concerned and over what have been previously proposed, our analytical results show impressive improvements. As such, through our proposed queuing model, the required decoder's buffer is substantially smaller of what that obtained by a prior model, considering the same networking parameters, which prompts decreasing the average frame waiting time. Copyright © 2015 John Wiley & Sons, Ltd.

Low-complexity high-throughput decoding architecture for convolutional codes

Sequential decoding can achieve a very low computational complexity and short decoding delay when the signal-to-noise ratio (SNR) is relatively high. In this article, a low-complexity high-throughput decoding architecture based on a sequential decoding algorithm is proposed for convolutional codes. Parallel Fano decoders are scheduled to the codewords in parallel input buffers according to buffer occupancy, so that the processing capabilities of the Fano decoders can be fully utilized, resulting in high decoding throughput. A discrete time Markov chain (DTMC) model is proposed to analyze the decoding architecture. The relationship between the input data rate, the clock speed of the decoder and the input buffer size can be easily established via the DTMC model. Different scheduling schemes and decoding modes are proposed and compared. The novel high-throughput decoding architecture is shown to incur 3-10% of the computational complexity of Viterbi decoding at a relatively high SNR.

Soft Decision Fano Decoding of Block Codes Over Discrete Memoryless Channel Using Tree Diagram

Soft Decision Fano Decoding of Block Codes Over Discrete Memoryless Channel Using Tree DiagramA novel low complexity soft decision technique which allows the decoding of block codes with tree structure is proposed. These codes are shown to have a convenient tree structure that allows Fano decoding techniques to be used to decode them. The Fano algorithm searches through the tree structure of the block code for a path which has the optimal value of the Fano metric function. When a new candidate codeword is found, an optimality check is performed on it by using the threshold. If checked successfully, the candidate codeword is the most likely codeword and the search stops. The basic idea of this approach is to achieve a good error performance progressively in a minimum number of steps. For each decoding step, the error performance is tightly bounded and the decoding is terminated at the stage where either optimum or near optimum error performance is achieved. As a result, more flexibility in the trade off between performance and decoding complexity is provided. Some examples of the tree construction and the soft decision Fano decoding procedure are discussed.

High Throughput Parallel Fano Decoding

In this paper, a bidirectional Fano algorithm (BFA) is proposed, in which a forward decoder (FD) and a backward decoder (BD) search in the opposite direction in the code tree simultaneously. It is shown that the proposed BFA can achieve more than twice the decoding throughput compared to the conventional unidirectional Fano algorithm (UFA) and there is higher throughput improvement at low signal-to-noise ratio (SNR). This new BFA decoding technique is applied in the parallel convolutional decoding architecture in very high throughput systems, such as the WirelessHD system. Due to the variability in the decoding delays of the parallel codewords, a scheduler is introduced in the parallel Fano decoding architecture which can dynamically allocate the idle decoders to assist with decoding the other parallel codewords in a bidirectional manner. It is shown that the proposed parallel Fano decoding with scheduling can dramatically increase the decoding throughput compared to the parallel Fano decoding without scheduling, and its computational complexity is much lower than that of parallel Viterbi decoding, especially at high SNR. The performance of the parallel Fano decoding with different scheduling schemes is also compared and analyzed in detail in the paper.

Incorporating automatic repeat request and thresholds with variable complexity decoding algorithms over wireless networks: queuing analysis

Wireless networks are spreading very fast compared to wired-based networks because of its ease in installation, lower cost, reduced dependence on infrastructure and support for emerging mobile and sensing applications. Unfortunately, wireless channels are less efficient in carrying much of data. Moreover, they are characterised by having lower signal-to-noise ratio, resulting in more corrupted packets. Consequently, the performance of such networks may be severely affected due to invoking transmission control protocol (TCP) congestion algorithms whenever a packet is lost. The authors propose a novel queuing model that utilises Fano decoding and automatic repeat request (ARQ) to reduce the drawbacks of TCP in wireless networks. The proposed model describes how received packets are corrected based on Fano decoding mechanism and how the retransmission of corrupted packets is performed. The major aim of proposing this queuing model, when ARQ is totally incorporated, is to find a generic form expression for the average system capacity. The proposed model is validated through simulation in which the results show perfect agreement with those of the analytical model. The authors do not stop to this extent, but rather verify the correctness of the results through comparing them with those obtained in the previous work, where the mechanism of ARQ was completely neglected.

Evaluation of channel adaptive access point systemwith Fano decoding

The popularity of wireless networks is increasing due to their mobility, flexibility, and scalability. High error rate over wireless channels leads current transmission control protocol congestion algorithms to be maintained. Finding approaches at lower layers to overcome this is very efficient and powerful. However, Fano decoding is an efficient error correction mechanism, especially in wireless networks, due to its capability of being adaptive to the channel. In this paper, Stop-and-wait with hybrid automatic repeat request using Fano decoding is adopted at the link layer. Consequently, we propose novel analytical and numerical studies for the distribution of packets in the system of wireless access point or base station. Moreover, the capacity of a sufficient access point system is evaluated numerically.

Queuing Analysis and Simulation of Wireless Access and End Point Systems using Fano Decoding

Wireless networks are a growing technology due to its ability to receive data in areas where it is very hard to plug-in using wires. TCP Reno assumes in his congestion algorithms that the packet loss is the major cause of network congestion. In wireless networks, this is not correct because having a high bit error rate leads also to a packet loss. Link layer approach is one of the most efficient proposed solutions to maintain TCP over wireless networks. For example, having hybrid ARQ type 1 with Fano decoding, which is an error correction technique, is very appropriate and is of concern in wireless networks due to its capability of offering decoding steps, which are dependent to the channel state. In this paper, we propose a novel queuing model to see the effect of employing Fano decoding on the buffer of wireless access or end points since it is a very effective network parameter and cannot be neglected. Our queuing model is concerned not only about those departed packets after being decoded using Fano algorithm, but also the way packets arrive to the wireless access or end point systems. An analytical study has been conducted to derive a general form expression for the average number of packets residing in the system’s buffer. On the other hand, a simulation study using programming language has been performed to validate our analytical results.

Adaptive computation control of variable complexity fano decoders

We propose a novel computation control method for variable-complexity Fano decoders with buffers. Our method substantially lowers the rates of data block loss associated with conventional Fano decoders. For reasonably large buffer sizes, our method outperforms Layland's buffer management scheme with block loss rates close to the theoretical lower bound.

An Asynchronous Low-Power High-Performance Sequential Decoder Implemented With QDI Templates

This paper presents the design of a channel-based asynchronous sequential decoder implemented with quasi-delay-insensitive templates. The Powermill simulation results in TSMC 0.25-CMOS technology show that the circuit runs at 430 MHz and consumes 32 mW. Techniques to effectively partition and implement the top level design, the implementation of fast shift registers, memories, and various other structures are discussed. Compared to a previously designed synchronous Fano decoder, the asynchronous version consumes 1/3 the power and runs at 2.15 times the speed assuming standard process normalization. The design also highlights the introduction of a standard-cell library and back-end design flow for asynchronous designs based on precharged half buffer (PCHB) templates

Fano Decoding with Timeout: Queueing Analysis

In mobile communications, a class of variable-complexity algorithms for convolutional decoding known as sequential decoding algorithms is of interest since they have a computational time that could vary with changing channel conditions. The Fano algorithm is one well-known version of a sequential decoding algorithm. Since the decoding time of a Fano decoder follows the Pareto distribution, which is a heavy-tailed distribution parameterized by the channel signal-to-noise ratio (SNR), buffers are required to absorb the variable decoding delays of Fano decoders. Furthermore, since the decoding time drawn by a certain Pareto distribution can become unbounded, a maximum limit is often employed by a practical decoder to limit the worst-case decoding time. In this paper, we investigate the relations between buffer occupancy, decoding time, and channel conditions in a system where the Fano decoder is not allowed to run with unbounded decoding time. A timeout limit is thus imposed so that the decoding will be terminated if the decoding time reaches the limit. We use discrete-time semi-Markov models to describe such a Fano decoding system with timeout limits. Our queuing analysis provides expressions characterizing the average buffer occupancy as a function of channel conditions and timeout limits. Both numerical and simulation results are provided to validate the analytical results.

A unified framework for tree search decoding: rediscovering the sequential decoder

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm is decomposed into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form matched to the search stage. We argue that the forward and feedback (matrix) filters of the minimum mean-square error decision feedback equalizer (MMSE-DFE) are instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for solving underdetermined linear systems and using lattice reduction methods to diminish complexity, at the expense of a marginal performance loss. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well-known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSE-DFE Fano decoder is established via simulation results and analytical arguments in several multiple-input multiple-output (MIMO) and intersymbol interference (ISI) scenarios.

Convolutional coding for finite-state channels

We propose new decoders for decoding convolutional codes over finite-state channels. These decoders are sequential and utilize the information about the channel state sequence contained in the channel output sequence. The performance of these decoders is evaluated by simulation and compared to the performance of memoryless decoders with and without interleaving. Our results show that the performance of these decoders is good whenever the channel statistics are such that the joint estimate of the channel state sequence and the channel input sequence is good, as, for example, when the channel is bursty. In these cases using even a partial search decoder such as the Fano decoder over the appropriate trellis is nearly optimal. However, when the information between the output sequence and the sequence of channel states and inputs diminishes, the memoryless decoder with interleaving outperforms even the optimal decoder which knows the channel state.

Computing the performance of Fano and stack decoders using importance sampling

An exact analysis method for the evaluation of the bit error rate of coded communication systems which employ the Fano and stack decoders is presented. The proposed method is an extremely efficient importance sampling scheme which substantially reduces the required number of conventional Monte Carlo simulation runs.

Performance of Modified-Fano Algorithm in Adaptive-Variable-Rate Transmission System over Fading Channels

Ideas of feedback, adaptive transmission and coding have been combined to improve the performance of communication systems over the Rayleigh fading channel with slow and flat fading assumption. The coded variable-rate transmission systems employ the Fano and the modified Fano algorithms for decoding [1]. The simulation study of the uncoded variable-rate bipolar signalling with continuous rate adaptation over an infinite range shows that such a system can completely nullify the effect of fading. A four-rate uncoded systems is only 0.5 dB inferior and the two-rate coded system with either Modified-Fano or Fano decoding is only 0.4 dB inferior to the ideal infinite rate systems at a BER of 10-5. The increase in the average rate of transmission of both coded and uncoded variable rate systems is found to degrade the error performance. For the coded systems both the Fano and Modified-Fano algorithms provide the similar error performance but the Modified-Fano decoder provides the throughput advantage over the Fa...