Browsing by Subject "Successive cancellation decoding"

Now showing 1 - 4 of 4

Open Access
Channel combining and splitting for cutoff rate improvement
(Institute of Electrical and Electronics Engineers, 2006) Arikan, E.
The cutoff rate R0(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W1, W2, the capacity function always satisfies C(W1) + C(W2) ≤ C(W), while there are examples for which R0(W1) + R0(W2) > R0(W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper.
Open Access
Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
(IEEE, 2009) Arikan, E.
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W) of any given binary-input discrete memoryless channel (B-DMC) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN (i): 1 ≤ i ≤ N} becomes large, the fraction of indices i for which I(WN (i) is near 1 approaches I(W) and the fraction for which I(WN (i) is near 0 approaches 1 - I(W). The polarized channels WN (i) are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) and any target rate R < I(W), there exists a sequence of polar codes {Cn;n ≥ 1 such that Cn has block-length N = 2n, rate ≥ R, and probability of block error under successive cancellation decoding bounded as Pe (N, R) ≤ O(N-1/4 independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.
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
Systematic polar coding
(IEEE, 2011) Arikan, E.
Polar codes were originally introduced as a class of non-systematic linear block codes. This paper gives encoding and decoding methods for systematic polar coding that preserve the low-complexity nature of non-systematic polar coding while guaranteeing the same frame error rate. Simulation results are given to show that systematic polar coding offers significant advantages in terms of bit error rate performance.