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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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Precoding matrix for MIMO

My question is according to the precoding matrix for open loop and closed loop capacity. For open loop spatial multiplexing transmission, co CSI is available at the transmitter Tx, that is equivalent ...
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0answers
9 views

decoding process/ Space time block coding

I have doubts about understanding a decoding procedure in STBC ( Tarock code). How I have read, the decoding procedure is similar to the Alamouti scheme. I have taken the codeword from a book "...
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1answer
34 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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29 views

How to decode the received sequence by using convolutional code with generator matrix and Viterbi algorithm?

Consider the discrete memoryless channel with input alphabet $𝐴_𝑋 = ${$0,1$}, output alphabet $𝐴_Y=${$0,𝛼,𝛽,1$}, and transition probabilities: \begin{array}{} & 0 & \...
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22 views

Is there any FEC algorithm that can even cover up parity byte(bit) error?

Although there are many Forward error correction algorithms available, I couldn't find algorithm that can recover error even when the part of parity byte (or bit) is also damaged while transmission. ...
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24 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
50 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
76 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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19 views

Optimal Channel Bit Allocation For Branches

The Question Hi. I was asked to solve this problem. I solved the part a but could not be able to solve the b part. Also found that $(\frac{2(1+p)^2}{(1+p)(1-p)})^2 = \frac{{{\sigma_\theta}_1}^2}{{...
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22 views

Why can Generalized eigenvector algorithm for blind equalization be used in SIMO?

I have a question as mentioned the title. I don't know if it's possible to use the Generalized eigenvector algorithm for blind equalization in SISO, but in most of papers I've read, they are talking ...
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1answer
45 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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51 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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0answers
64 views

Wrap Around Viterbi Algorithm for tail biting decoding “WAVA”

Tail-biting where the initial and final states of the encoder are identical. Tail biting is done by initializing the shift register contents with the last m information bits in the input block to ...
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0answers
32 views

Recursive systematic convolutional code with TCM

My question is: What are the outputs from the TCM encoder ?
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0answers
23 views

Are there forward error correction codes specifically designed for low SNR reception?

Or are there codes that happen to work particularly well when the SNR is below (perhaps much below) 1? I'm interested in both rateless and block codes.
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1answer
74 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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18 views

Measuring bit-error rate or block-error rate when simulating block code?

(I realize this is a somewhat 'subjective' question -- I am actually asking about what is the common practice or convention.) We have blocks (or 'words') of $k$ information bits each. The probability ...
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2answers
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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1answer
191 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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0answers
53 views

Cliff effect due to Forward Error Correction

I've implemented GMSK modulator and demodulator given in figure.4 and figure.5 of this paper successfully. But when I use AWGN channel with FEC in it, the performance of BER curve is showing cliff ...
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1answer
77 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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10 views

creating a adjacency matrix using photographs for Quasi cyclic LDPC codes

I'm trying to figure out how create the adjacency matrix ,$\Gamma$, starting from a protograph/base graph but I'm a bit confused on how to do this. For example, lets say my base graph is as follows $$...
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1answer
21 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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2answers
1k 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
26 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
28 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
41 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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0answers
42 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 ...
3
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2answers
478 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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0answers
86 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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69 views

HDPC on RaptorQ

I am trying to implement RaptorQ based on the standard (https://tools.ietf.org/html/rfc6330). I have implemented most of the algorithm but I don’t have a way to validate its correctness. More ...
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1answer
400 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
134 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
74 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
57 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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1answer
658 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
98 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
1k 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
727 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
218 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
128 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
1k views

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
118 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
99 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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2answers
334 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
87 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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1answer
38 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
172 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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1answer
46 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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0answers
141 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 ...