Lossy Joint Source-Channel Coding in the Finite Blocklength Regime

We study the problem of lossless joint sourcechannel coding (JSCC) in the finite block length regime from an unequal message protection (UMP) perspective. We demonstrate that the problem of lossless JSCC can be cast in terms of UMP codes previously studied. We show that an optimal JSCC can be constructed from a matched UMP code. We further derive a finite block length bound that characterizes the performance of a JSCC constructed from a UMP code not perfectly matched to the source. This bound is evaluated for a binary memoryless source transmitted over a binary symmetric channel. Two-class schemes previously studied in literature are compared with the proposed scheme. Empirically the JSCCs based on UMP codes approach the performance of the optimal matched code quite fast in number of classes used.

Benefiting from the advantage of joint source-channel coding in the finite block length regime and the advancement of AI technologies, deep joint source channel coding (DJSCC) has been extensively investigated for various sources (e.g., text source, image source, and video source) and achieved remarkable performance in limited bandwidth and low signal-to-noise ratios (SNRs). However, the performance gain brought by DJSCC methods is all observed via simulations in literature, where synchronization, channel estimation and the power amplifier are assumed to be perfect. In this paper, we design a software-defined radio (SDR) based platform to validate the DJSCC method for image transmission in real wireless scenarios.

Conventionally, posterior matching is investigated in channel coding and block encoding contexts – the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols progressively arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback. We propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">instantaneous encoding phase</i> that operates during the symbol arriving period and achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. During the instantaneous encoding phase, the evolving message alphabet is partitioned into groups whose priors are close to the capacity-achieving distribution, and the encoder determines the group index of the actual sequence of symbols arrived so far and applies randomization to exactly match the distribution of the transmitted index to the capacity-achieving one. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage in terms of the reliability function. For streaming over a symmetric binary-input DMC, we propose a one-phase <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">instantaneous small-enough difference (SED) code</i> that not only achieves the JSCC reliability function, but also, thanks to its single-phase time-invariant coding rule, can be used to stabilize an unstable linear system over a noisy channel. For equiprobably distributed source symbols, we design low complexity algorithms to implement both the instantaneous encoding phase and the instantaneous SED code. The algorithms group the source sequences into sets we call types, which enable the encoder and the decoder to track the priors and the posteriors of source sequences jointly, leading to a log-linear complexity in time. While the reliability function is derived for non-degenerate DMCs, i.e., DMCs whose transition probability matrix has all positive entries, for degenerate DMCs, we design a code with instantaneous encoding that achieves zero error for all rates below Shannon’s joint source-channel coding limit.

Packet loss is a common phenomenon in current image processing (IP) networks. Current network protocols manage this problem by retransmitting the lost packets. However, the delay due to the retransmission of the lost packets may be inappropriate for many real-time applications. Therefore, a better approach to resolve this problem is to recover the lost data from the received packets using some error control coding scheme. The conventional error control coding is based on a tandem source and channel coding framework, where the message signal is first compactly represented using a rate-distortion criterion, and then, the error correcting bits are appended to it. As an alternative, joint source-channel codes that can perform as good as, or better than, the tandem source and channel coding are being considered. In particular, lowpass discrete Fourier transform (DFT) codes have been studied as joint source-channel codes. This paper is dedicated to the analysis of lowpass DFT codes with bursty erasures. The analysis aims at studying the performance of lowpass DFT codes when consecutive samples of a DFT codevector are erased due to packet losses. It is known that lowpass DFT codes are highly sensitive to quantization error when there are consecutive erasures. This phenomenon is studied in the context of syndrome decoding. Bursty erasures give rise to a syndrome-decoding matrix that has very large elements depending on the code parameters and the burst length. The size of the elements of the syndrome decoding matrix is studied by establishing various relationships between the syndrome decoding matrix and the parity and the generator polynomial coefficients. With a suitable model for the quantization error, the reconstruction error performance of lowpass DFT codes is analyzed and then applied to the case of bursty erasures. The paper also proposes a recursive syndrome decoding algorithm to improve on the normal syndrome decoding of lowpass DFT codes in the case of bursty erasures. The proposed algorithm aims at recovering the quantized values of the erased samples based on a cost computed using the statistics of the codevector and of the quantization error.

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We extend the results of Ghourchian et al. [1] to joint source-channel coding with eavesdropping. Our work characterizes the sequential encoding process using the cumulative rate distribution functions (CRDF) and includes a security constraint using the cumulative leakage distribution functions (CLF). The information leakage is defined based on the mutual information between the source and the output of the wiretap channel to the eavesdropper. We derive inner and outer bounds on the achievable CRDF for a given source and CLF, and show that the bounds are tight when the distribution achieving the capacity of the wiretap channel is the same as the one achieving the capacity of the channel.

To reduce the system complexity, cost, and overall processing time, the adoption of joint source-channel coding (JSCC) has been found to be popular. Among several options, universal filtered multi-carrier (UFMC) is regarded as the dominant contender and alternative to orthogonal frequency division multiplexing (OFDM) for upcoming wireless mobile communication networks. UFMC provides increased spectral efficiency, less peak to average power ratio (PAPR), and lower bit error rate (BER) with the removal of the cyclic prefix (CP) and grouping of subcarriers. Multiple-input and multiple-output (MIMO) technology is known to improve the capacity and throughput significantly of wireless systems. In this paper, the authors analyze the performance of UFMC techniques with Kaiser filter and Dolph-Chebyshev filter combined with JSCC in 32x32 large MIMO set-up, which provides better PAPR, power spectral density (PSD), less BER with increased channel capacity. The experimental aspects have been discussed and the results are derived using simulation mimicking near real-life situations.

Recently, Altug and Wagner [1] posed a question regarding the optimal behavior of the probability of error when channel coding rate converges to the capacity sufficiently slowly. They gave a sufficient condition for the discrete memoryless channel (DMC) to satisfy a moderate deviation property (MDP) with the constant equal to the channel dispersion. Their sufficient condition excludes some practically interesting channels, such as the binary erasure channel and the Z-channel. We extend their result in two directions. First, we show that a DMC satisfies MDP if and only if its channel dispersion is nonzero. Second, we prove that the AWGN channel also satisfies MDP with a constant equal to the channel dispersion. While the methods used by Altug and Wagner are based on the method of types and other DMC-specific ideas, our proofs (in both achievability and converse parts) rely on the tools from our recent work [2] on finite-blocklength regime that are equally applicable to non-discrete channels and channels with memory.

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT) codes in the non-asymptotic regime. In that work, achievability is based on an infinite-length random code and decoding is attempted at every symbol. The coding rate backoff from capacity due to channel dispersion is greatly reduced with feedback, allowing capacity to be approached with surprisingly small expected latency. This paper is concerned with VLFT codes based on finite-length codes and decoding attempts only at certain specified decoding times. Note that with an underlying finite-length code, the transmitter may have to repeat code symbols. The penalties of using a finite block-length N and a sequence of specified decoding times are studied. This paper shows that properly scaling N with the expected latency can achieve the same performance up to second order terms as with N =∞. The penalty introduced by limiting the decoding is a constant term and hence the performance approaches capacity as expected latency increases as long as the interval between periodic decoding times grows sub-linearly with the expected latency.

Orthogonal frequency-division multiplexing (OFDM) signaling format is commonly associated with guard subintervals to reject interblock interference (IBI) and enable simple one-tap frequency-domain equalization (FDE) at the receiver when received over dispersive channels. Despite the advantages, the insertion of guard subintervals expands the signal spectrum and thus trades off the spectral efficiency significantly. In this paper, the nonguarded OFDM (NG-OFDM) signaling format, which is exactly OFDM without inserting guard subintervals, is considered to avoid the spectrum expansion and combined with spectral precoding to further achieve high spectrum compactness. In particular, spectral precoders are designed for NG-OFDM to provide very small spectral sidelobes, and thus extremely compact signal spectrum, and associate the transmitted waveform with low peak-to-average power ratio. To reject IBI among received NG-OFDM blocks over dispersive channels, a guard subinterval in each received block is removed at the receiver, and this turns the resultant receiver as nonorthogonal over subcarrier subchannels, thus resulting in intercarrier interference (ICI). The corresponding channel capacity and linear minimum-mean-square-error (LMMSE) data estimation are analyzed. It is shown that the proposed spectrally precoded NG-OFDM (SP-NG-OFDM) system can provide channel capacity very close to nonprecoded and spectrally precoded OFDM using the cyclic prefix (CP-OFDM) when the removal guard ratio is small, and much higher channel capacity per unit bandwidth than spectrally precoded CP-OFDM conveying the same data rate provided that a small out-of-band power proportion is required. When a sufficiently small precoding rate is adopted, the SP-NG-OFDM receiver, using guard removal and LMMSE-FDE, is also shown to counteract ICI effectively and exploit frequency diversity over dispersive channels.

The Gaussian distribution and its related functions are widely used in statistics, engineering, and physics, including hypothesis testing, quality control, and digital communications. As the standard normal cumulative distribution function (CDF) lacks a closed-form, accurate approximations are essential for practical applications. This study presents new, highly accurate improvements to existing approximations of the standard normal distribution function while preserving simplicity. The proposed methodology refines current formulas by introducing additional parameters and systematically optimizing them using R-based iterative procedures guided by the Kolmogorov-Smirnov statistic to minimize maximum and mean absolute errors. Evaluations across a dense grid confirm the precision and robustness of the proposed models. Results demonstrate significant improvements, with one enhancement reducing the maximum error by a factor of 4.86 compared to previous models, while other formulas show notable accuracy gains. The improved models remain straightforward to implement, making them suitable for real-time engineering and applied statistical computations. A practical application is demonstrated by calculating the bit error rate (BER) in Binary Phase Shift Keying (BPSK) systems under Gaussian noise, where the proposed approximations closely replicate the exact BER curve, confirming their effectiveness in telecommunications system analysis. These improvements provide engineers and scientists with precise, efficient tools, supporting modeling, risk assessment, and system reliability in applications requiring accurate Gaussian evaluations.

In this work, we obtain lower and upper bounds on the maximal {transmission} rate at a given codeword length $n$, average probability of error $\epsilon$ and power constraint $\bar{P}$, over a finite valued, block fading additive white Gaussian noise (AWGN) channel with channel state information (CSI) at the transmitter {and the receiver}. {These bounds characterize} deviation of the finite blocklength coding rates from the channel capacity which is in turn achieved by the \textit{water filling} power allocation across time. {The bounds obtained also} characterize the rate enhancement possible due to the {CSI} at the transmitter in the finite blocklength regime. The results are further elucidated via numerical examples.

Digital communication systems offer high data rate and efficient transmission through the channel. Low bit error rates assess the quality of any communication system. Bit Errors occur as the result of Adjacent Channel Interference (ACI), Co¬Channel Interference (CCI) and Inter Symbol Interference (ISI) in the presence of Noise. These interferences are more prominent in mobile cellular systems owing to dispersive nature of the channel. Channel dispersion is attributable to multiple reflections in Mobile cellular systems. Equalizer technique is one of the important methods of countering the ill effects of channel. The response of the equaliser should be closely inverse of the channel response. Then the interferences are reduced to great extent by proper equalizers in the receiver end. It attempts to recover the original transmitted symbols at the receiver. In the absence of Channel knowledge, Adaptive equalizer offers superior performance. In this paper, Steepest Descent algorithm is discussed. This algorithm applied in Adaptive equaliser for time invariant and Mobile cellular channels. The efficiency of above algorithm in terms of Bit Error Rate versus SIR is analysed for both channels.

This paper considers simultaneous wireless information and power transfer (SWIPT) mechanisms in a relaying network with finite blocklength (FBL) codes. The reliability of the network is optimized under both a power splitting (PS) protocol and a proposed joint PS and time switching (TS) protocol. Under both protocols, we first determine the overall error probability formulation of the SWIPT-enabled two-hop transmission in the FBL regime. Subsequently, we state and solve optimization problems minimizing the overall error probability. Via numerical analysis, we show the appropriateness of our analytical model and demonstrate the performance advantage of the proposed protocol in comparison to TS and PS protocols. In addition, we provide interesting insights on the system behavior by characterizing the impact of the blocklength, transmit power and packet size on the reliability performance.

We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of multi-view discrete memoryless channels and then extend our results to general multi-view channels (using multi-letter formulas). We argue that the channel capacity and dispersion of such multi-view channels converge exponentially fast in the number of views to the entropy and varentropy of the input distribution, respectively. We identify the exact rate of convergence as the smallest Chernoff information between two conditional distributions of the output, conditioned on unequal inputs. For the special case of the deletion channel, we compute upper bounds on this Chernoff information. Finally, we present a new channel model we term the Poisson approximation channel — of possible independent interest — whose capacity closely approximates the capacity of the multi-view binary symmetric channel for any fixed number of views.