Searcharxiv⌕ Search

arXiv subjects

Mustafa Cemil Coşkun

Publications and source records attributed to Mustafa Cemil Coşkun.

14 recordsLinked to original sources

Enhanced Feedback Mechanisms for Resource-Efficient Incremental Redundancy

Incremental redundancy (IR) can reduce error rates by spreading coded bits across multiple transmission attempts. However, conventional stop-and-wait operation with coarse feedback often over-provisions retransmissions, triggers unnecessary decoding attempts, and increases end-to-end latency. This paper develops enhanced feedback and scheduling mechanisms that predict the additional redundancy needed for successful decoding and allocate only the required resources. We study two complementary strategies. First, using channel statistics, we learn a one- or two-shot mapping from channel quality to the minimum redundancy budget. As a byproduct, we derive an achievable reliability lower bound on the error probability of hybrid automatic repeat request (HARQ) systems. Numerical results with polar-coded IR-HARQ scheme show that the bound can be closely approached by appropriately selecting the second-transmission redundancy over a wide SNR range with savings up to 60\% in retransmission size. Second, we propose a realization-aware early-feedback mechanism that uses first-transmission reliability information to make per-codeword decisions before decoding: whether the codeword is already decodable, if not, how many additional redundancy versions are needed, or whether decoding is unlikely and rate adaptation is preferable. Link-level simulations with 5G NR LDPC codes show that both predictors achieve high accuracy (about 96\% in our study), increasing the probability of successful decoding within at most two transmission occasions.

cs.IT↗

Error Detection Based on Generalized Successive Cancellation List Decoding for Polar Codes

Successive cancellation list (SCL) decoding has been widely adopted for polar codes, which allows near maximum likelihood performance with sufficiently large list size. In this work, we show that, if the list size is $2^γ$, where $γ$ is the fundamental quantity called mixing factor, then a modification to SCL decoding can implement Forney's generalized decoding rule. Hence, it provides an efficient means to discard unreliable decisions. The performance achieved by short polar codes under the proposed generalized SCL decoding is analyzed via Monte Carlo simulations.

cs.IT↗

Precoded Polar Product Codes

Precoded polar product codes are proposed, where selected component codes enable successive cancellation list decoding to generate bit-wise soft messages efficiently for iterative decoding while targeting optimized distance spectrum as opposed to eBCH or polar component codes. Rate compatibility is a byproduct of $1$-bit granularity in the component code design.

cs.IT↗

Successive Cancellation Ordered Search Decoding of Modified $\boldsymbol{G}_N$-Coset Codes

A tree search algorithm called successive cancellation ordered search (SCOS) is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding with adaptive complexity for transmission over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is needed to terminate decoding; therefore, SCOS also applies to $\boldsymbol{G}_N$-coset codes modified with dynamic frozen bits. The average complexity is close to that of successive cancellation (SC) decoding at practical frame error rates (FERs) for codes with wide ranges of rate and lengths up to $512$ bits, which perform within $0.25$ dB or less from the random coding union bound and outperform Reed--Muller codes under ML decoding by up to $0.5$ dB. Simulations illustrate simultaneous gains for SCOS over SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average complexity at various SNR regimes. SCOS is further extended by forcing it to look for candidates satisfying a threshold, thereby outperforming basic SCOS under complexity constraints. The modified SCOS enables strong error-detection capability without the need for an outer code. In particular, the $(128, 64)$ polarization-adjusted convolutional code under modified SCOS provides gains in overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic SC flip decoding at high SNR.

cs.IT↗

An Information-Theoretic Perspective on Successive Cancellation List Decoding and Polar Code Design

This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless symmetric (BMS) channels. It also provides upper and lower bounds for these quantities that can be computed efficiently for very long codes. For the binary erasure channel (BEC), we provide a simple method to estimate the mean accurately via density evolution. The analysis shows how to modify, e.g., Reed-Muller codes, to improve the performance when practical list sizes, e.g., $L\in[8, 1024]$, are adopted. Exemplary constructions with block lengths $N\in\{128,512\}$ outperform polar codes of 5G over the binary-input additive white Gaussian noise channel. It is further shown that there is a concentration around the mean of the logarithm of the required list size for sufficiently large block lengths, over discrete-output BMS channels. We provide the probability mass functions (p.m.f.s) of this logarithm, over the BEC, for a sequence of the modified RM codes with an increasing block length via simulations, which illustrate that the p.m.f.s concentrate around the estimated mean.

cs.IT↗

Complexity-Adaptive Maximum-Likelihood Decoding of Modified $\boldsymbol{G}_N$-Coset Codes

A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive cancellation (SC) decoding for practical error rates when applied to polar codes and short Reed-Muller (RM) codes, e.g., block lengths up to $N=128$. By modifying the algorithm to limit the worst-case complexity, one obtains a near-ML decoder for longer RM codes and their subcodes. Unlike other bit-flip decoders, no outer code is needed to terminate decoding. The algorithm can thus be applied to modified $\boldsymbol{G}_N$-coset code constructions with dynamic frozen bits. One advantage over sequential decoders is that there is no need to optimize a separate parameter.

cs.IT↗

Successive Cancellation Decoding of Single Parity-Check Product Codes: Analysis and Improved Decoding

A product code with single parity-check component codes can be described via the tools of a multi-kernel polar code, where the rows of the generator matrix are chosen according to the constraints imposed by the product code construction. Following this observation, successive cancellation decoding of such codes is introduced. In particular, the error probability of single parity-check product codes over binary memoryless symmetric channels under successive cancellation decoding is characterized. A bridge with the analysis of product codes introduced by Elias is also established for the binary erasure channel. Successive cancellation list decoding of single parity-check product codes is then described. For the provided example, simulations over the binary input additive white Gaussian channel show that successive cancellation list decoding outperforms belief propagation decoding applied to the code graph. Finally, the performance of the concatenation of a product code with a high-rate outer code is investigated via distance spectrum analysis. Examples of concatenations performing within $0.7$ dB from the random coding union bound are provided.

cs.IT↗

Polar-Coded Non-Coherent Communication

A polar-coded transmission (PCT) scheme with joint channel estimation and decoding is proposed for channels with unknown channel state information (CSI). The CSI is estimated via successive cancellation (SC) decoding and the constraints imposed by the frozen bits. SC list decoding with an outer code improves performance, including resolving a phase ambiguity when using quadrature phase-shift keying (QPSK) and Gray labeling. Simulations with 5G polar codes and QPSK show gains of up to $2$~dB at a frame error rate (FER) of $10^{-4}$ over pilot-assisted transmission for various non-coherent models. Moreover, PCT performs within a few tenths of a dB to a coherent receiver with perfect CSI. For Rayleigh block-fading channels, PCT outperforms an FER upper bound based on random coding and within one dB of a lower bound.

cs.IT↗

Successive Cancellation Inactivation Decoding for Modified Reed-Muller and eBCH Codes

A successive cancellation (SC) decoder with inactivations is proposed as an efficient implementation of SC list (SCL) decoding over the binary erasure channel. The proposed decoder assigns a dummy variable to an information bit whenever it is erased during SC decoding and continues with decoding. Inactivated bits are resolved using information gathered from decoding frozen bits. This decoder leverages the structure of the Hadamard matrix, but can be applied to any linear code by representing it as a polar code with dynamic frozen bits. SCL decoders are partially characterized using density evolution to compute the average number of inactivations required to achieve the maximum a-posteriori decoding performance. The proposed measure quantifies the performance vs. complexity trade-off and provides new insight into dynamics of the number of paths in SCL decoding. The technique is applied to analyze Reed-Muller (RM) codes with dynamic frozen bits. It is shown that these modified RM codes perform close to extended BCH codes.

cs.IT↗

Ternary Quantized Polar Code Decoders: Analysis and Design

The performance of short polar codes under successive cancellation (SC) and SC list (SCL) decoding is analyzed for the case where the decoder messages are coarsely quantized. This setting is of particular interest for applications requiring low-complexity energy-efficient transceivers (e.g., internet-of-things or wireless sensor networks). We focus on the extreme case where the decoder messages are quantized with 3 levels. We show how under SCL decoding quantized log-likelihood ratios lead to a large inaccuracy in the calculation of path metrics, resulting in considerable performance losses with respect to an unquantized SCL decoder. We then introduce two novel techniques which improve the performance of SCL decoding with coarse quantization. The first technique consists of a modification of the final decision step of SCL decoding, where the selected codeword is the one maximizing the maximum-likelihood decoding metric within the final list. The second technique relies on statistical knowledge about the reliability of the bit estimates, obtained through a suitably modified density evolution analysis, to improve the list construction phase, yielding a higher probability of having the transmitted codeword in the list. The effectiveness of the two techniques is demonstrated through simulations.

cs.IT↗

Successive Cancellation List Decoding of Product Codes with Reed-Muller Component Codes

This letter proposes successive cancellation list (SCL) decoding of product codes with Reed--Muller (RM) component codes. SCL decoding relies on a product code description based on the $2\times 2$ Hadamard kernel, which enables interpreting the code as an RM subcode. The focus is on a class of product codes considered in wireless communication systems, based on single parity-check and extended Hamming component codes. For short product codes, it is shown that SCL decoding with a moderate list size performs as well as (and, sometimes, outperforms) belief propagation (BP) decoding. Furthermore, by concatenating a short product code with a high-rate outer code, SCL decoding outperforms BP decoding by up to $1.4$ dB.

cs.IT↗

Efficient Error-Correcting Codes in the Short Blocklength Regime

The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach the theoretical bounds with various performance versus decoding complexity tradeoffs.

cs.IT↗

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.

cs.IT↗

Successive Cancellation Decoding of Single Parity-Check Product Codes

We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding.

cs.IT↗