Questions tagged [channelcoding]

Questions related to channel coding, forward error correction, code performance calculations, and decoding algorithms. Typical code examples are Hamming codes, cyclic codes, BCH, Reed-Solomon, turbo codes, and LDPC.

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35 views

Channel encoding after digital modulation

Generally, when using channel encoding followed by interleaving, that process should be performed before the modulator and the system structure should be like that : For me, I only use the ...
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15 views

Bad performance of Trellis-Code for low SNR

I have computed the BER-curves for a trellis code with different block lengths in Matlab (using bertool). For small values of $E_b/N_0$, the bit error rate is even worse than without any channel ...
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Minimum value of G (Amplitude) that guarantees an error probability of at least $10^{-2}$ in a 32-PAM transmission system

pretty much new here. This question comes from an Online course quiz which i have already completed but cant seem to get a good sleep over, just because i cant figure it out. Below is the question ...
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2answers
27 views

Interleaving or randomisation?

I am trying to implement a digital communication system as a learning exercise. For error correction, I am using two concatenated codes (RS and convolutional). However, I read that, in order to reduce ...
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54 views

Is MMSE equalizer necessary?

For observation $y$, channel coefficient $h$ and gaussian noise $w \sim \mathcal{CN}(0,\sigma^2)$, $$y = hx + w \tag{1}$$ Note that for OFDM system, (1) is assumed channel input-ouput equation on ...
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Channel coding simulation

I’m new to channel coding, and I’m trying to learn about channel coding in general, and iterative turbo coding in particular. I was trying to play with some simulink examples while reading to get a ...
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76 views

Update rule in Soft Output Viterbi Algorithm (SOVA) -Hagenauer rule

Soft output of SOVA, suggested by Hagenauer http://www.cse.lehigh.edu/~jingli/teach/S2003turbo/notes/SOVA.pdf , says in 2.2.2 "The Soft-Output Viterbi Algorithm" that $L_{j}^{\verb|^|}:= f(L_{j}^{\...
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1answer
44 views

Understanding Asymptotic Equipartition Property

I have some problems in understanding the precise meaning of the Asymptotic Equipartition Property, related to a large number n of independent and identically distributed random variables (X1, X2, ...,...
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46 views

Definition of Perfect Code (and example of Hamming Code)

Let's consider the following sentences about coding a message before transmitting it in a communication system (here you find the complete pdf) First question: can you explain me these two ...
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1answer
37 views

Notes or books to quickly get started on the basics of signal processing or wireless communication

I'll soon start working in signal processing, specially wireless communication systems. Hence I'd like to get a quick understanding of MIMO and related systems, for example, the topics like: 1) where ...
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31 views

Doubts about Huffman and Shannon - Fano Coding

I was reading these slides about Source Coding and I have the following questions: 1) Let's consider this part: Can you explain me step by step the reasons of a, b, c? Which is the general rule to ...
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2answers
309 views

Nyquist noiseless channel capacity; how can bit-rate be two times the bandwidth?

I'm confused by the Nyquist channel capacity formula. How can channel maximum capacity approach double the bandwidth. $C = 2\times BW \times log_{2}(L)$ bits/sec The way it was explained to me ...
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30 views

Trellis Termination (zero termination) scheme for RSC encoder

I am currently try to implement a simple RSC encoder in Matlab. As far as I know, this type of channel coding scheme require to reach an all-zero state in the encoder memory element(shift register). ...
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37 views

How to recover 2*Zc systematic bits punctured in LDPC?

In 5G NR LDPC encoder 2Zc systematic bits are punctured at the transmitter end. At the receiver end, it is able to recover all bits excluding the punctured bits at the transmitter end. As the ...
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41 views

How to detect missing bit position in a bit-stream?

I'm trying to establish a one-way communication and facing problem in the receiver end because of some missing bits. For example, if the sender sends 100 bits the receiver received 95/96 bit. Now the ...
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33 views

Convolutional Code: choosing a trellis and puncture pattern for code 2/3

I'm working on convolutional coding in which I'm using generator polynomials as {13, 15} with puncture pattern of {1 1 0 1} for code rate 2/3. I don't get expected BER trend. If I use puncture ...
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1answer
19 views

How good is the Leech lattice for AWGN coding or MSE quantization of Gaussian sources?

Anyone know where to find graphs showing how well it works vs other schemes? thanks
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Convolutional coding that payload length does not change

This is the question about Sigfox radio specification. The stack: Specifically, in Section 3.10 of the specification, we have a convolutional coding (after CRC) with three possible polynominals. I ...
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1answer
91 views

Maximizing entropy on a channel

In Shannon's paper "A Mathematical Theory of Communication", in Theorem 8 he states: Theorem 8: Let the system of constraints considered as channel have a capacity $C = \log W$. If we assign $$p^{(s)}...
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29 views

convolutional coding with higher order QAM

I've implemented a simple 1/2 rate convolutional code and a viterbi decoder algorithm. I followed the most-common type of convolutional coding implementation I could find by googling: 1 input bit gets ...
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2answers
154 views

Getting the bitstream of an unknown RF signal

I am trying to get the bitstream of a signal sent over 433MHz. I have installed SDR# (I'm on Windows), connected my NESDR SMART, and I identified the signal here: I can see there is only one peak ...
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1answer
57 views

rate 1/128 channel code for 5 bits of information

I need to construct channel code for 5 bits of information for a wireless channel. Possible code rate could be as low as 1/128 (very reliable). At decoder I assume to use channel LLRs as decoder input ...
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1answer
198 views

GNU Radio | Async FEC encoder/decoder loopback | Issue during decoding?

I have implemented a loopback flowgraph intending to perform the following: FEC encode (repetition code) an input stream in16_2.dat Store the encoded stream as <...
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1answer
44 views

operations valid for predicting new codewords for a Linear block code having linear encoder mapping

I want to know which operations are valid for predicting/finding a new codeword from a set of known codewords for a linear block code having linear encoder mapping, for eg.: Consider a linear ...
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1answer
120 views

Berlekamp–Massey algorithm verification

I'm implementing Berlekamp–Massey algorithm for BCH codes, but I have some troubles with it: I don't realize how to verify this algorithm. Is there any methods to prove, that code works correctly or ...
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2answers
39 views

Sampling vs repetition code

I'm working on a multiuser wireless system simulation and have run into something regarding sampling rates. From everything I've known for a matched filter receiver, the correlation step is performed ...
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1answer
71 views

Error detection and correction algorithms for Wireless Body Area Networks

I am working on transmitting ECG signals over wireless body area network based on IEEE 802.15.4 standard. To reduce the BER and increase the signal reconstruction quality, I think that I need to ...
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1answer
40 views

Adaptive Predictive Coding: Transmit signal AND prediction coefficients

I'm not well versed in the literature so please forgive/inform me if my terminology is wrong: I have a bounded real-valued, discrete-time signal $x_n \in \mathbb [0, 1]$, and I want to (lossily) ...
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1answer
214 views

Is there better than hamming code for correcting errors

As known, hamming code can be represented by (7,4) where data are 4 bits, and 3 bits for parity, and (15,11) where 11 bits are data and 4 bits for parity. It can correct up to one bit, or detect two ...
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1answer
44 views

Why $H(A)=H(C)$ where $C$ is $A$ with an additional parity bit?

Let $A=\{00,01,10,11\}$ with equal probabilities for each symbol, and $B=\{0, 1\}$ be a parity generator such that $$ b=\begin{cases} 0, & \text{if} \,\, a=00 \quad \text{or} \quad a=11 \\ 1, &...
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37 views

Applying BCJR equalization for LDPC encoded information

I want to apply BCJR decoder for LDPC encoded information. How can I change the BCJR originally for convolutional codes for this purpose?
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1answer
141 views

Is it possible to generate Hamming code with minimum distance $d$ which can correct more than 1 bit error?

In literature, all I am seeing is Hamming code with minimum Hamming distance $3$. Theoretically a Hamming code with minimum distance d can detect $d-1$ errors and can correct $(d-1)/2$ error. So ...
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1answer
95 views

Unambiguously detecting (not correcting) between $t+1$ and $2t$ errors in a Reed-Solomon message

I know that Reed-Solomon codes of the form $(N,N-2t)$ can correct up to $t$ errors, and detect up to $2t$ errors, but I've only seen the correction procedure: Berlekamp-Massey or Euclidean to get the ...
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1answer
150 views

Viterbi Algorithm - Selecting survivor paths which both contain the same Hamming distance

To my (limited) knowledge, when determining which survivor path to choose to produce an error-corrected output of a binary Viterbi decoder, the path with the smallest Hamming distance is the most ...
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0answers
101 views

Convolutional FEC decoding - is it necessary to know where a decoding block begins and ends with convolutional codes?

I understand that the difference between convolutional and block-based FEC is that convolutional codes can be used in a continuous stream – however every implementation I saw still uses blocks. So I ...
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2answers
122 views

Alamouti Scheme. MISO. STBC for real constellation

I have a real orthogonal design for codeword... $$ \begin{bmatrix} s1 & s2 \\ -s2 & s1 \end{bmatrix} $$ $$ s=\begin{bmatrix} s1\\ s2 \end{bmatrix} $$ $$ Y^T=\sqrt{\frac{P}{Mt}} h^T ...
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2answers
34 views

Which channel coding technique is suitable for wireless SPIHT compressed image: Reed-Solomon or convolutional code?

I want to transmit a SPIHT-based (Set Partitioning In Hierarchical Trees) image compressed image over a wireless fading channel, which will be suitable as channel coding technique: Reed-Solomon or ...
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1answer
388 views

Shannon capacity with distribution different from Gaussian

If I understand correctly, in AWGN channel, for a given SNR, there is a code for $M$ input codeword $\mathbf{X}_{i, 1 \leq i \leq M}$ that $$\lim_{n \to \infty} R=\lim_{n \to \infty}\frac{\log(M)}{n} ...
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1answer
253 views

why did convolution coding achieve BER less than Reed-Solomon?

I tried convolutional coding and Reed-Solomon (RS) (block coding technique) for wireless channel where the input data is bitstream. Convolutional coding achieved lower BER comparing with RS. If the ...
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1answer
27 views

Computing overall bitrate of a transmitter with a two chunks package

I'm programming a digital communication system in MATLAB and I have a two chunk package, let's say a header and a body, and I'm using a different channel code for each chunk, i. e. BHC1 and BCH2. But ...
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3answers
3k views

Capacity of cascade binary symmetric channels

Let's imagine that we have interconnected in cascade $L$ binary symmetric channels each with the same transition probability $p(y|x) \in \{p, q=1-p\}$, where the output of each BSC is connected to the ...
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1answer
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Why GCD(1+D, 1+D^2) = 1+D?

I'm reading Digital Communications, Proakis, and in order to classify an encoder as catastrophic or noncatastrophic I need the GCD of the elements in the generator G(D). I don't really know what kind ...
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1answer
31 views

Inter-symbol energy coding

I have scoured my entire library and I can't find where I read about a method of using symbol energy intentionally smeared across multiple bit times in such a way that the symbols can be recovered ...
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1answer
72 views

Does Hamming encoding preserve orthogonality?

The question I have is this-- if I have two binary vectors, i.e. $x_1, x_2 \in \mathbb F_2^k$ that are orthogonal, i.e. $x_1^T x_2 = 0$, and let's say I Hamming encode each of them separately with an $...
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57 views

Viterbi equalization of Fibonacci coding

I'm working a Viterbi equalizer for a BPSK signal which uses Fibonacci coding. In the more theoretical descriptions of the Viterbi algorithm I've read, there's a term for the probability of a ...
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2answers
732 views

Confusion in Channel Encoding and Convolutional Encoding

If I'm making NRZ signal by first encoding 1 input bit into 10 bits multiplied by -V/+V before sending it into a channel, is it called channel encoding? If I then modulated it using GMSK technique, ...
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164 views

Convolving a signal with the impulse response of the channel

For a complex signal x to be transmitted over a channel with complex impulse response h, x will be convolved with h. What will the mathematical operation done in the reveiver to cancel the effect of h?...
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1answer
821 views

Maximum Throughput of QAM system

Consider a QAM system designed to transmit over a bandwidth of $3 \ \mathrm{kHz}$. The channel's power constraint imposes a maximum $\mathrm{SNR}$ of $30 \ \mathrm{dB}$. The system can tolerate a ...
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1answer
199 views

Question about symbol detection in ISI channels (use of APP decoder in Matlab)

I am studying the problem of digital symbols detection in ISI channel. In the figure below, the output symbol is represented as a weighted sum of input symbols. I am trying to use MAP decoder ...
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1answer
101 views

How does a Huffman encoded message gets unified before channel encoding?

I aim to understand the signal entire transmission pipeline. Currenlty, I am facing a problem regarding the handling of a Huffman encoded message. Example: Message $X$ contains symbols $a(50\%)$, $...