Browsing by Subject "List decoding"

Now showing 1 - 6 of 6

Open Access
Decoding strategies at the relay with physical-layer network coding
(Institute of Electrical and Electronics Engineers, 2012) Bhat, U.; Duman, T. M.
A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large.
Open Access
An FPGA implementation architecture for decoding of polar codes
(IEEE, 2011) Pamuk, Alptekin
Polar codes are a class of codes versatile enough to achieve the Shannon bound in a large array of source and channel coding problems. For that reason it is important to have efficient implementation architectures for polar codes in hardware. Motivated by this fact we propose a belief propagation (BP) decoder architecture for an increasingly popular hardware platform; Field Programmable Gate Array (FPGA). The proposed architecture supports any code rate and is quite flexible in terms of hardware complexity and throughput. The architecture can also be extended to support multiple block lengths without increasing the hardware complexity a lot. Moreover various schedulers can be adapted into the proposed architecture so that list decoding techniques can be used with a single block. Finally the proposed architecture is compared with a convolutional turbo code (CTC) decoder for WiMAX taken from a Xilinx Product Specification and seen that polar codes are superior to CTC codes both in hardware complexity and throughput. © 2011 IEEE.
Open Access
Lossless polar compression of g-ary sources
(IEEE, 2013) Çaycı, Semih; Arıkan, Orhan
In this paper, lossless polar compression of g-ary memoryless sources in the noiseless setting is investigated. Polar compression scheme for binary memoryless sources, introduced by Cronie and Korada, is generalized to sources over prime-size alphabets. In order to reduce the average codeword length, a compression scheme based on successive cancellation list decoding is proposed. Also, a specific configuration for the compression of correlated sources is considered, and it is shown that the introduced polar compression schemes achieve the corner point of the admissible rate region. Based on this result, proposed compression schemes are extended to arbitrary finite source alphabets by using a layered approach. © 2013 IEEE.
Open Access
Performance and computational analysis of polarization-adjusted convolutional (PAC) codes
(2022-06) Moradi, Mohsen
We study the performance of sequential decoding of polarization-adjusted con- volutional (PAC) codes. We present a metric function that employs bit-channel mutual information and cutoff rate values as the bias values and significantly re- duces the computational complexity while retaining the excellent error-correction performance of PAC codes. With the proposed metric function, the computa- tional complexity of sequential decoding of PAC codes is equivalent to that of conventional convolutional codes. Our results indicate that the upper bound on the sequential decoding compu- tational complexity of PAC codes follows a Pareto distribution. We also employ guessing technique to derive a lower bound on the computational complexity of sequential decoding of PAC codes. To reduce the PAC sequential decoder’s worst-case latency, we restrict the number of searches executed by the sequential decoder. We introduce an improvement to the successive-cancellation list (SCL) decod- ing for polarized channels that reduces the number of sorting operations without degrading the code’s error-correction performance. In an SCL decoding with an optimum metric function, we show that, on average, the correct branch’s bit- metric value must be equal to the bit-channel capacity. On the other hand, the average bit-metric value of a wrong branch can be at most 0. This implies that a wrong path’s partial path metric value deviates from the bit-channel capacity’s partial summation. This enables the decoder to identify incorrect branches and exclude them from the list of metrics to be sorted. We employ a similar technique to the stack algorithm, resulting in a considerable reduction in the stack size. Additionally, we propose a technique for constructing a rate profile for PAC codes of arbitrary length and rate which is capable of balancing the error- correction performance and decoding complexity of PAC codes. For signal-to- noise ratio (SNR) values larger than a target SNR value, the proposed approach can significantly enhance the error-correction performance of PAC codes while retaining a low mean sequential decoding complexity. Finally, we examine the weight distribution of PAC codes with the goal of providing a new demonstration that PAC codes surpass polar codes in terms of weight distribution.
Open Access
Serially concatenated polar codes
(Institute of Electrical and Electronics Engineers, 2018) Arikan, E.
Simulation results show that the performance of polar codes is improved vastly by using polar codes as inner codes in serially concatenated coding schemes. Furthermore, this performance improvement is achieved using a relatively short cyclic redundancy check as the outer code and a practically implementable successive cancellation list decoder for decoding the overall code. This paper offers a theoretical analysis of such schemes by employing a random-coding method on the selection of the outer code and assuming that the channel is memoryless. It is shown that the probability of error for the concatenated coding scheme decreases exponentially in the code block length at any fixed rate below the symmetric capacity. Applications of this result include the design of polar codes for communication systems that require high reliability at small to moderate code lengths, such as control channels in wireless systems and machine-type communications for industrial automation.
Open Access
Some results on zero-error capacity under list decoding
(IEEE, 1990) Arıkan, Erdal
Summary form only given. A number of questions recently raised by Elias regarding a zero-error list-of-L code have been addressed. It has been shown that computing the zero-error capacity of the channel with feedback is NP-complete, and bounds on the size of the code have been obtained.