Designing robust and efficient codes for reliable communication in noisy environments is a key challenge. Recent advancements show that deep learning-based channel codes can outperform traditional handcrafted ones in certain scenarios. Despite recent advancements, most state-of-the-art codes are trained using the binary cross-entropy (BCE) loss, LBCE, which aims to optimize bit error rate (BER) but is less effective at minimizing block error rate (BLER) – a critical metric for avoiding costly re-transmissions in wireless systems. To address this limitation, we first apply several recently-proposed BLER-specific loss functions to train channel autoencoders, i.e., to design both the neural encoder and the matched neural decoder. Our results show that the application of such loss functions improves the design of autoencoders, compared to the conventional BCE loss, especially when BLER is the performance metric of interest. Next, we introduce a novel loss function, called the adaptively-scaled norm (ASN) loss, LASN, which dynamically adjusts penalties based on the error rates across the bit positions, making it more effective for BLER minimization. Compared to existing methods, the proposed loss function promotes a lower variance for the contribution from different bit positions while still emphasizing more on the bit positions with higher chances of error. Using a two-step process of pre-training and fine-tuning, we show that LASNoutperforms LBCEand the existing BLER-minimizing loss functions across various communication channels.

This paper presents a novel methodology for designing the reliability sequence π for polarization-adjusted convolutional (PAC) and polar codes. Given a sequence π of length N, a family of nested information sets is constructed for N codes. The design objective is to minimize the average of the minimum signal-to-noise ratios (SNRs) required to achieve a target block error rate (BLER) across these nested codes. To reduce the search space, the N bit positions are partitioned into M components of length N/M, with bit positions within each component following a predefined reliability order. The design problem is then formulated as a Markov decision process (MDP) and solved using a deep Q-network (DQN) with an experience replay buffer. Simulation results under CRC-aided successive cancellation list (CA-SCL) decoding for nested polar codes show that the proposed sequence improves SNR performance over existing nested polar codes, including those used in 5G. Additionally, nested PAC codes under successive cancellation list (SCL) decoding with the proposed π outperform nested PAC and polar codes based on the known reliability sequences, under SCL or CA-SCL decoding. Moreover, individual PAC codes extracted from the nested family perform competitively with the best-known PAC/polar codes designed for specific rates. The proposed method is applicable to various precoded polar code constructions and decoding algorithms. The observed performance improvements, particularly in PAC codes, suggest that this approach is a promising candidate for future communication systems, including 6G.

This paper introduces a novel rate-profile design for Polarization-Adjusted Convolutional (PAC) codes by simplifying the construction of an information set (inf set) for a PAC code of length$N$into the design of inf sets for$M$component codes of length$\frac{N}{M}$. We define a Markov Decision Process (MDP) that formulates the task of identifying the inf set that minimizes the Block Error Rate (BLER). To achieve this, we employ a Deep QNetwork (DQN) with an experience replay buffer to determine the optimal inf set with the lowest BLER. Simulation results demonstrate that under Successive Cancellation List (SCL) decoding, our designed PAC codes improve BLER compared to state-of-the-art PAC codes. This method is not limited to the design of PAC code inf set; it is applicable to inf set design for the general family of precoded Polar codes and supports any decoder.

We propose a channel auto-encoder which incorporates the encoding and decoding structure of classical generalized concatenated code (GCC) based on polar codes. The outer encoder and decoder of classical GCC polar codes are implemented by non-linear functions parameterized with a transformer based neural network. Our results show that the proposed scheme results in enhanced reliability of classical polar codes under SC decoding.

Turbo Autoencoder (TAE) is a deep-learning based channel code that demonstrates promising error correction performance. This paper studies the rate-matching problem for TAE and proposes a rate-matched TAE framework. The rate-matched TAE is a single auto-encoder model that can be used for multiple code rates. It matches the code rate of a mother$(3k, k)$TAE to a desired code of parameters ($n^{\ast}, k^{\ast}$) by using a combination of freezing message bits, repeating code symbols, and puncturing code symbols. We refer to the conventional TAE with message word length$k$and code length$3k$as mismatched TAE. The rate-matched TAE shares the same encoder and decoder structure with mismatched TAE but is trained to jointly optimize the performance across multiple rates. We study two important hyper-parameters for the rate-matched TAE: puncturing pattern and training signal-to-noise ratio (SNR) for constituent rates. Three puncturing patterns, namely, head, tail, and uniform puncturing are proposed and evaluated. Training SNRs are determined according to a heuristic method that uses test loss as a performance metric. Our simulation results show that the rate-matched TAE for$k= 100$and rates$r\in \{0.1, 0.2, \ldots, 0.9\}$significantly outperforms the mismatched TAE when$r\geq 0.4$.

This paper evaluates the performance of Turbo Autoencoder (TurboAE), an end-to-end jointly trained neural channel encoder and decoder, for different well-known inter-leavers over additive white Gaussian noise (AWGN) channel. TurboAE and Turbo codes share structural similarities. Therefore, in search of suitable interleavers for TurboAE, it is important to examine the interleavers designed for Turbo codes. In this paper, different interleavers are compared for TurboAE, and it is shown that using interleavers such as Quadratic Permutation Polynomial (QPP) and S-random interleavers provides considerable performance gain. The interleaver gain is achieved for both TurboAE made of convolutional neural network (CNN) layers and TurboAE made of recurrent neural networks (RNN) layers. Certain techniques are also proposed to enhance the performance of TurboAE RNN.

In this paper, we present list autoencoder (listAE) to mimic list decoding used in classical coding theory. With listAE, the decoder network outputs a list of decoded message word candidates. To train the listAE, a genie is assumed to be available at the output of the decoder. A specific loss function is proposed to optimize the performance of a genie-aided (GA) list decoding. The listAE is a general framework and can be used with any AE architecture. We propose a specific architecture, referred to as incremental-redundancy AE (IR-AE), which decodes the received word on a sequence of component codes with non-increasing rates. Then, the listAE is trained and evaluated with both IR-AE and Turbo-AE. Finally, we employ cyclic redundancy check (CRC) codes to replace the genie at the decoder output and obtain a CRC aided (CA) list decoder. Our simulation results show that the IR-AE under CA list decoding demonstrates meaningful coding gain over Turbo-AE and polar code at low block error rates range.

There have been significant research activities in recent years to automate the design of channel encoders and decoders via deep learning. Due the dimensionality challenge in channel coding, it is prohibitively complex to design and train relatively large neural channel codes via deep learning techniques. Consequently, most of the results in the literature are limited to relatively short codes having less than 100 information bits. In this paper, we construct ProductAEs, a computationally efficient family of deep-learning driven (encoder, decoder) pairs, that aim at enabling the training of relatively large channel codes (both encoders and decoders) with a manageable training complexity. We build upon the ideas from classical product codes, and propose constructing large neural codes using smaller code components. More specifically, instead of directly training the encoder and decoder for a large neural code of dimension k and blocklength n, we provide a framework that requires training neural encoders and decoders for the code parameters (n1,k1) and (n2,k2) such that n1n2= n and k1k2= k. Our training results show significant gains, over all ranges of signal-to-noise ratio (SNR), for a code of parameters (225,100) and a moderate-length code of parameters (441,196), over polar codes under successive cancellation (SC) decoder. Moreover, our results demonstrate meaningful gains over Turbo Autoencoder (TurboAE) and state-of-the-art classical codes. This is the first work to design product autoencoders and a pioneering work on training large channel codes.

This paper enhances the performance and training of the Turbo Autoencoder (TurboAE), an end-to-end jointly trained neural channel encoder and decoder. A novel interleaver for TurboAE with convolutional neural network (CNN) is proposed, which is shown to enhance the end-to-end performance of both TurboAE continuous and binary. Thanks to the proposed interleaver, TurboAE binary performs better than a benchmark Turbo code of length 100. In addition, a novel additional term to the loss function is proposed to improve the pairwise distance distribution of the codewords, which is shown to help the training convergence of TurboAE with CNN and recurrent neural network (RNN).

The throughput of successive cancellation decoding of polar codes can be improved through simplified decoders that identify specific constituent codes in the decoding tree. The identified codes include rate-0, rate-1, repetition, and single parity-check codes. In this work, constituent codes that belong to the family of first-order Reed-Muller codes, and their sub-codes, are also identified in the decoding tree. Alternative decoding schemes that utilize the structure of Reed-Muller codes are incorporated into successive cancellation decoding. Simulation results show that such an approach can improve both the block error rate performance as well as the decoding latency of polar codes.

In this paper, a localization-based polar construction method is proposed to directly find the set of synthetic channels for information bits given a code configuration. Taking advantage of the partial order of polar codes, only a small number of synthetic channels need to be ordered, which scales as O(N/ log23/2 N), resulting in a sublinear complexity to construct a polar code. Specifically, a practical method is put forward first to fast construct a group-based partial order diagram. A local area in the diagram with adaptive boundaries is then identified. By ordering the synthetic channels within the local area and combining selected ones with all the synthetic channels beyond the local area, the final set of synthetic channels for information bits are determined. Simulation results demonstrate how to adapt the boundary settings to different rate matching schemes and code configurations, and validate the effectiveness of the proposed method compared with the density evolution based methods.

Recently convolutional polar (cpolar) codes have been proposed. A tensor-network-based successive cancellation (SC) decoding was proposed for them under which cpolar codes were shown to outperform polar codes. In this paper we present the notion of m-bit-channels for cpolar codes and give the recursive construction of m-bit-channels for m=3. Then a log likelihood ratio(LLR)-based SC decoding of complexity order O(Nlog(N)) for cpolar codes is presented. We also present the numerical results for performance evaluation of cpolar codes under SC list (SCL) decoding. Our simulation results show that cpolar codes can achieve the performance of polar codes with a list size reduced by a factor of 4.

We construct polar codes for the specific purpose of incremental redundancy hybrid automatic repeat request (IR-HARQ) schemes. The rate compatibility of our scheme is ensured by both puncturing and extending of the code. A new puncturing algorithm for polar codes is proposed, and we develop an algorithm for finding good extending sequences for polar codes from any arbitrary punctured rate, with the goal of improving the throughput as much as possible. Simulation results for different types of puncturing and extending algorithms are presented. We show how the proposed extending algorithm, when properly operated with a good puncturing algorithm and a well-chosen puncturing rate, yields IR-HARQ coding schemes which can operate within 1 dB of Shannon capacity over a very wide range of signal-to-noise ratios.

The design of an efficient hybrid automatic repeat request (ARQ) scheme based on rate compatible low density parity check (LDPC) codes is considered. It has been shown that extending as well as puncturing of LDPC codes can produce good rate compatible LDPC codes for the additive white Gaussian noise channel. One issue with the traditional LDPC-based hybrid ARQ methods is that the throughput drops off significantly at low signal-to-noise ratios (SNRs). In this paper we introduce a coding scheme which is capable of using puncturing, extending and feedback at the same time to address this issue. Appropriate choice of feedback functions along with optimum combining of received signals for the belief propagation decoder mitigates the throughput drop- off issue at low SNRs, while having a small feedback overhead from the receiver. A powerful mother code is generated via the progressive edge growth algorithm and is used for puncturing and extending in the proposed scheme. Clustering the codewords of the longest codebook is used to decrease the overhead of the feedback connection. Simulation analysis of the throughput shows that our scheme could get as close as 0.5 dB to the Shannon limit while having up to 2 dB gain compared to previous works at low SNRs.

In many signal processing applications including Audio and speech processing as well as other research areas of diagnosis of failures in rotating machinery, finding a compact representation of observations signals is often highly desirable. In this respect, chirplets have recently been introduced as an efficient tool for signal representation. However, determining the required number of chirp atoms for the perfect estimation of an observed signal is of great importance. In this research work we study the chirplets signal decomposition to find a compact representation for audio signals of music and speech. The number of chirplets to be used is determined by using the state-of-the-art information criteria. Simulation and experimental results show that by using 4 chirplets are enough for accurate signal representation of music while about 7 to 9 chirplets suffices for speech signal reconstruction. As another application the evaluations are also made on vibration signals. Finally, extracted chirplet atoms are employed to reconstruct the observed signals of music and speech. Subjective tests show acceptable results for signal reconstruction.