Seyyed Ali Hashemi

A Fast Polar Code List Decoder Architecture Based on Sphere Decoding

Polar codes are a recently discovered family of capacity-achieving error-correcting codes. Among the proposed decoding algorithms, successive-cancellation list decoding guarantees the best error-correction performance with codes of moderate lengths, but it yields low throughput. Speed-up techniques have been proposed in the past: most of them rely on approximations that degrade the error-correction capability of the algorithm. We propose a speed-up technique for successive-cancellation list decoding of polar codes that is exact for list size of 2, while its approximations bring negligible error-correction performance degradation (<;0.05 dB) for other list sizes. A decoder architecture is designed: the proposed technique increases the throughput of a factor of 3.16×, at the cost of 14.2% in area occupation.

Partitioned successive-cancellation list decoding of polar codes

Successive-cancellation list (SCL) decoding is an algorithm that provides very good error-correction performance for polar codes. However, its hardware implementation requires a large amount of memory, mainly to store intermediate results. In this paper, a partitioned SCL algorithm is proposed to reduce the large memory requirements of the conventional SCL algorithm. The decoder tree is broken into partitions that are decoded separately. We show that with careful selection of list sizes and number of partitions, the proposed algorithm can outperform conventional SCL while requiring less memory.

Simplified Successive-Cancellation List decoding of polar codes

The Successive-Cancellation List (SCL) decoding algorithm is one of the most promising approaches towards practical polar code decoding. It is able to provide a good trade-off between error-correction performance and complexity, tunable through the size of the list. In this paper, we show that in the conventional formulation of SCL, there are redundant calculations which do not need to be performed in the course of the algorithm. We simplify SCL by removing these redundant calculations and prove that the proposed simplified SCL and the conventional SCL algorithms are equivalent. The simplified SCL algorithm is valid for any code and can reduce the time-complexity of SCL without affecting the space complexity.

List sphere decoding of polar codes

Polar codes have gained a lot of attention during the past few years, because they can provably achieve the capacity of a memoryless channel. The design of efficient polar code decoders has been an active topic of research. The simple Successive Cancellation (SC) decoding algorithm yields poor error correction performance on short polar codes: the SC- List (SCL) algorithm overcomes this problem, but its hardware implementation requires a large amount of memory. Sphere Decoding (SD) is an alternative decoding technique that has been shown to work well for short polar codes, but it is burdened by undesirable characteristics. The performance of SD strongly depends on the choice of a suitable sphere radius, whose value must be selected according to the conditions of the channel. Channel conditions also affect the algorithms time complexity, that is consequently variable. In this paper, we introduce a List- SD algorithm for short polar codes. It has a fixed time complexity and does not make use of a radius: thus, no knowledge of the channel noise level is required. It is shown that the error correction performance of List-SD can match that of SC and SCL with as low as 72% of their memory requirements.

Blind Detection With Polar Codes

In blind detection, a set of candidates has to be decoded within a strict time constraint, to identify which transmissions are directed at the user equipment. We propose a blind detection scheme based on polar codes, where the radio network temporary identifier is transmitted instead of some of the frozen bits. A low-complexity decoding phase decodes all candidates, selecting a subset that is decoded by a high-performance algorithm. Simulations results show good missed detection and false alarm rates, that meet the 3GPP LTE-A and future 5G standard specifications. We also propose an early stopping criterion that can reduce the number of operations performed, improving both average latency and energy consumption. The detection speed is analyzed and different system parameter combinations are shown to meet the stringent timing requirements, leading to various implementation trade-offs.

Matrix reordering for efficient list sphere decoding of polar codes

The Successive-Cancellation List (SCL) algorithm is one of the best polar code decoding algorithms in terms of trade-offs between complexity and error correction performance. The List-Sphere Decoding (List-SD) algorithm has been recently proposed: it yields a better complexity/performance trade-off than SCL in the decoding of short polar codes, that can be used as component codes for larger polar codes. We exploit the structure of the generator matrix of polar codes to propose a matrix reordering technique which allows to significantly reduce the List-SD complexity without degrading its error correction performance, further improving the aforementioned trade-off. The proposed technique is implemented on hardware and it is shown that at the same Frame Error Rate (FER) and Bit Error Rate (BER), the matrix reordering can reduce the resource requirements of List-SD of up to 73%. Furthermore, FER and BER curves are plotted for case studies, showing that at the same complexity cost, matrix reordering improves the performance of List-SD of up to 0.75 dB at FER=10-2.

A Novel Discrete Particle Swarm Optimization for FRM FIR Digital Filters

This paper presents a novel discrete particle swarm optimization (PSO) for frequency response masking (FRM) finite impulse response (FIR) digital filters over the canonical signed-digit (CSD) multiplier coefficient space. A look-up table (LUT) scheme is employed to ensure that the PSO automatically searches through permissible CSD multiplier coefficient values in the course of optimization without any recourse to backtracking. This is achieved by searching through the indices of the CSD multiplier coefficient values in the LUT instead of the coefficient values themselves. In this way, the resulting multiplier coefficient values are ensured to conform to a prespecified wordlength as well as to a prespecified maximum number of non-zero digits. The salient feature of this LUT scheme is that by introducing barren layers in the LUT, there is no need to limit the search space manually in the course of PSO to prevent from going over the boundaries of the search space. Examples are given to illustrate the application of the proposed PSO to the design and optimization of a lowpass and a bandpass FRM FIR digital filters.

Fast Simplified Successive-Cancellation List Decoding of Polar Codes

Polar codes are capacity achieving error correcting codes that can be decoded through the successive-cancellation algorithm. To improve its error-correction performance, a list-based version called successive-cancellation list (SCL) has been proposed in the past, that however substantially increases the number of time-steps in the decoding process. The simplified SCL (SSCL) decoding algorithm exploits constituent codes within the polar code structure to greatly reduce the required number of time-steps without introducing any error-correction performance loss. In this paper, we propose a faster decoding approach to decode one of these constituent codes, the Rate-1 node. We use this Rate-1 node decoder to develop Fast-SSCL. We demonstrate that only a list-size-bound number of bits needs to be estimated in Rate-1 nodes and Fast-SSCL exactly matches the error-correction performance of SCL and SSCL. This technique can potentially greatly reduce the total number of time-steps needed for polar codes decoding: analysis on a set of case studies show that Fast-SSCL has a number of time- steps requirement that is up to 66.6% lower than SSCL and 88.1% lower than SCL.

A novel finite-wordlength particle swarm optimization technique for FRM IIR digital filters

A novel technique is presented for finite-wordlength (FW) particle swarm optimization (PSO) of BIBO stable FRM digital filters incorporating bilinear-LDI IIR interpolation subfilters. A novel LUT scheme is developed to ensure that the FWPSO automatically searches over permissible FW multiplier coefficient values only in the course of optimization. The salient feature of the proposed LUT scheme is that unlike the conventional PSO, there is no need to limit the search space in the course of optimization to prevent going over the boundaries of the search space. This is achieved by introducing barren layers in the LUTs. The usefulness of the proposed FWPSO is illustrated through its application to the design and simultaneous magnitude and group-delay optimization of a lowpass IIR-based FRM digital filter.

Particle swarm optimization of FRM FIR digital filters over the CSD multiplier coefficient space

This paper presents a novel technique for particle swarm optimization (PSO) of FRM FIR digital filters over the CSD multiplier coefficient space. In this technique, a FRM FIR digital filter is represented as a point in a multidimensional CSD multiplier coefficient space. In order to limit the search space, a CSD LUT is generated to include promising points in the multidimensional multiplier coefficient space. Candidate CSD FRM FIR digital filters generated in the course of particle swarm optimization are guaranteed to remain automatically within the CSD LUT boundaries during the constituent PSO move operation without any recourse to backtracking. This is achieved by augmenting the LUT with barren regions. An example is given to illustrate the application of the proposed PSO to the design of a lowpass FRM FIR digital filter.