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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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Parity Check matrix from degree and check nodes polynoms, LDPC codes

I'm trying to simulate LDPC codes which were optimized for the BEC channel. I generated the degree and check nodes polynomials according to chapter 3.15 in "Modern Coding Theory" by Richardson and ...
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43 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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Punctured Turbo Code Decoding: Convergence Issue

I have been trying to create a basic BCJR decoder for a rate (1/2) punctured turbo code. The puncturing is simple, the encoder alternatively selects between the parity bits generated by the two ...
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49 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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21 views

Two inputs channel capacity

Assume that we have an AWGN channel with two inputs (A,B) and the o/p is written as Y = A + g B + Z where Z is an independent Gaussian noise with zero mean and unit variance and g is a constant ...
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18 views

5G NR base matrix

The 5G NR specs for channel code are found here: https://www.etsi.org/deliver/etsi_ts/138200_138299/138212/15.02.00_60/ts_138212v150200p.pdf Starting on page 21 there is base matrix for the LDPC code ...
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11 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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10 views

Calculating the Channel state information for localization

I want to build a localization system using 4G LTE for a project. Intuitively, I can get the position measuring the time a signal leaves the Base Station to the User Equipment. Knowing that these ...
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76 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
32 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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58 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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19 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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66 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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38 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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28 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
62 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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84 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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79 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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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
96 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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29 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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249 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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100 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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24 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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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
32 views

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
29 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
51 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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50 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
603 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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107 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
505 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
161 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
85 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 $a(50\%)$, $...
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1answer
62 views

Why are some LDPC codes more immune to noise than others?

When one analyzes an LDPC code, it is usual to plot the BER versus the $E_b / N_0$. My questions are: Why are some LDPC codes better than others in terms of noise immunity? After all, they are just ...
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1k views

How to explain this BER vs SNR behaviour?

I wrote a script in MATLAB to simulate an LDPC created using an algorithm of a colleague of mine. The parity check-matrix is regular and has dimensions $1012 \times 1518$ and the code rate is $R=1/3$. ...
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1answer
108 views

resilient codes to phase shift

I need to define an encoding to beacon IDs. The codes are going to be periodic but in the receiver side I can have phase shifts so I' wondering the best way to decode: - 8 bits code groups that ...
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1answer
2k views

Recursive systematic convolutional code (RSC) realization in MATLAB

How can I implement $\rm RSC(2,1,2)$ in MATLAB? Can I use convenc function to build RSC? The convenc function has 2 arguments: ...
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3answers
959 views

Bose Chaudhuri Hocquenghem (BCH) vs Reed Solomon (RS) Error correcting codes and sound transmission channel modeling

I've implemented an acoustic based information transmission system using a bandwidth of 2 kHz and the band between 18.5 and 20.5 kHz. I'm trying to find the best error correcting code for it, in the ...
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1answer
271 views

Source and channel encoding

In information theory, there are two concepts that are widely used: source encoding and channel encoding. I'm afraid I may not be capable of expressing my doubts clearly, but the thing is that I don'...
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1answer
156 views

Mechanics of a matrix Interleaver

I am having trouble understanding exactly how the matrix interleaver. I have read the following page from MathWorks. In it, it gives the following example where "123456" is interleaved as "142536." ...
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3answers
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What is the theoretical probability of error for OOK transmission?

I am trying to simulate an optical wireless communication channel which uses OOK modulation. Looking at equation 14 in this literature, I found that: For electrical SNR at the receiver $$\textrm{...
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1answer
130 views

Fountain codes and LDPC codes

I am having a small clarification with the difference between LDPC and fountain codes. In LDPC codes, each parity bit is depenedent on numerous data bits. Isn't that similar to fountain codes as the ...
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1answer
148 views

Finding $E_b/N_0$ when coding rate is $R_c$

I would like to calculate $E_b/N_0$ when the code rate is $R_c$ for BPSK signal. What I got this $$ E_b/N_0= \frac{1}{2R_mR_c \sigma^2} $$ and that is the case also according to this page. $R_m=1$ ...
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437 views

Relationship between $E_b/N_0$ and $\rm SNR$ with channel coding

I would like to know what would be the relationship between $E_b/N_0$ and $\rm SNR$ when there is a coding rate of $R_c=K/N$. Normally when there is no channel coding according to this link. $$\...
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1answer
114 views

Adding AWGN noise with certain power

Assume I have a signal(BPSK) and it has a certain amplitude. I would like to add a noise with a certain power to it. Assume I am using coding rate Rc as well. One method I am thinking would be to ...
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54 views

Difference between sticky channel Poisson-repeat channel

I don't quite understand the difference between a sticky channel and Poisson-repeat channel. A sticky channel allows duplications of symbols sent over the channel, then the block structure at the ...
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1answer
197 views

Relationship between information retrieval and source separation in signal processing

In machine learning, for the task of classifying input data (called an example) which are in binary representation, $\mathbf{x}\in \mathbb{R}^D$, $\mathbf{x} \in \{0,1\}^D$ into its multiple class ...
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48 views

Do convolution encoders exist with two separate (independent) inputs?

Do convolution encoders exist with two separate (independent) inputs? I got the question in my mind when I saw the question attached here.
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150 views

Code rate in IEEE 802.11b (DSSS)

I would like to know what code rates for forward error correction the physical layer of IEEE 802.11b uses for the different supported data rates. So far I didn't find any source for that. Actually in ...