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.
105
questions
1
vote
1answer
33 views
Is there an optimal way to quantize log-likelihood ratios of an AWGN channel?
My understanding is that given an AWGN channel and BPSK modulation, an LDPC decoder that uses message passing takes as input log-likelihood ratios $L$ of the following form by Bayes' rule:
$$
L=\frac{...
2
votes
1answer
82 views
Verifying LDPC matrices in CCSDS blue book
My understanding is that LDPC is a linear block code such that its generator matrix $\mathbf{G}$ and parity check matrix $\mathbf{H}$ satisfy $\mathbf{GH}^T=0$.
I am using the CCSDS blue book here as ...
1
vote
1answer
55 views
What's the shortest possible code that correct all the single bit errors?
Suppose the original code is a 2-bit binary coding with 3 possible alphabet.
\begin{align}
a&\rightarrow 00\\
b&\rightarrow 10\\
c&\rightarrow 11
\end{align}
Is that $\operatorname{Hamming}...
0
votes
0answers
24 views
Output of encoder RS-code: analyze the results
I found some simulation results of RS-encoder. In the description are written the following:
“When the program implementation is run, the clock is set to high i.e.
‘1 ’ and reset is set to low i.e. ‘ ...
0
votes
0answers
12 views
Is there a procedure to build RLL code with arbitrary signature?
I am wondering if there is a procedure to build a generic $RLL(x, y)$ encoding.
This article seems to describe one, but I have compared it to the wiki page, and they do not seem to agree.
Has anyone ...
0
votes
0answers
54 views
Understanding of Reed Solomon code
We send the data in bytes to the RS Encoder block. The RS Encoder block encodes the data with the Reed Solomon (225,223) code. It waits for 223 bytes and after this encode them to make a codeword of ...
0
votes
1answer
40 views
Channel coder: Does encoder help? Input signal distortion:
I am studying the channel coding theory. The channel coder adds redundant information to the input signal, that helps a decoder to reconstruct the signal.
BUT: Can encoder help to eliminate effects ...
0
votes
1answer
34 views
code construction process in polar coding
Arikan in his paper (arXiv link or IEEE link) about polar coding, explains how you can force the channel to polarize by applying a linear transformation (the generator matrix). He calls this a split ...
0
votes
1answer
53 views
system bit rate vs channel coding
We are usually asked about the full system bit rate. However, we use channel encoding in practical systems, for example conventional coding with rate $(1/3)$. My question is about the full system bit ...
0
votes
2answers
89 views
Conventional channel coding/decoding
I am trying to understand the algorithms of channel coding. Regarding the conventional channel which is, for me, the easiest one to implement, I have a question regarding the output of its decoder.
...
0
votes
1answer
160 views
Setting Parity Check Matrix for LDPC channel coding
I am trying to implement the LDPC code for OFDM system, where I input data should be binary of length $1024$ and the output coded data of length $2048$ (means of rate 1/2).
As known in Matlab ...
3
votes
1answer
64 views
LDPC for channel coding
I am working on OFDM over harsh channel, so the channel coding is an essential thing for achieving a reliable communication.
According to my reading, LDPC is almost the best channel coding we can use ...
0
votes
1answer
25 views
Is there two version of ulaw and alaw encoding in audio compression?
I am new to encoding in audios and i have searched for ulaw and alaw and found there is conversion from audio to this encoding CCITT alaw/ulaw and as i have known alaw/ulaw belongs to ITUT group not ...
1
vote
0answers
68 views
Degrees of freedom in coding (for a communication channel)
I was reading on my lecture slides about how to achieve diversity (i.e. transmit more copies of the same message in order to avoid its corruption; this technique may be realized by repeating the ...
0
votes
1answer
54 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 ...
-1
votes
2answers
74 views
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 ...
0
votes
2answers
48 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 ...
1
vote
0answers
62 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 ...
2
votes
0answers
91 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}^{\...
1
vote
1answer
53 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, ...,...
0
votes
2answers
100 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 ...
1
vote
1answer
46 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 ...
1
vote
2answers
725 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 ...
0
votes
0answers
45 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 ...
0
votes
1answer
22 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
1
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0answers
18 views
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 ...
1
vote
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)}...
1
vote
0answers
36 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 ...
3
votes
2answers
200 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 ...
0
votes
1answer
63 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 ...
3
votes
1answer
288 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 <...
0
votes
1answer
88 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 ...
-1
votes
1answer
146 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 ...
0
votes
2answers
40 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 ...
0
votes
1answer
58 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) ...
0
votes
2answers
357 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 ...
1
vote
1answer
46 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
$$
b=\begin{cases}
0, & \text{if} \,\, a=00 \quad \text{or} \quad a=11 \\
1, &...
0
votes
0answers
40 views
Applying BCJR equalization for LDPC encoded information
I want to apply BCJR decoder for LDPC encoded information.
How can I change the BCJR originally for convolutional codes for this purpose?
1
vote
1answer
269 views
Is it possible to generate Hamming code with minimum distance $d$ which can correct more than 1 bit error?
In literature, all I am seeing is Hamming code with minimum Hamming distance $3$. Theoretically a Hamming code with minimum distance d can detect $d-1$ errors and can correct $(d-1)/2$ error. So ...
4
votes
1answer
101 views
Unambiguously detecting (not correcting) between $t+1$ and $2t$ errors in a Reed-Solomon message
I know that Reed-Solomon codes of the form $(N,N-2t)$ can correct up to $t$ errors, and detect up to $2t$ errors, but I've only seen the correction procedure: Berlekamp-Massey or Euclidean to get the ...
0
votes
1answer
188 views
Viterbi Algorithm - Selecting survivor paths which both contain the same Hamming distance
To my (limited) knowledge, when determining which survivor path to choose to produce an error-corrected output of a binary Viterbi decoder, the path with the smallest Hamming distance is the most ...
1
vote
0answers
110 views
Convolutional FEC decoding - is it necessary to know where a decoding block begins and ends with convolutional codes?
I understand that the difference between convolutional and block-based FEC is that convolutional codes can be used in a continuous stream – however every implementation I saw still uses blocks.
So I ...
0
votes
2answers
138 views
Alamouti Scheme. MISO. STBC for real constellation
I have a real orthogonal design for codeword...
$$
\begin{bmatrix}
s1 & s2 \\
-s2 & s1
\end{bmatrix}
$$
$$
s=\begin{bmatrix}
s1\\
s2
\end{bmatrix}
$$
$$
Y^T=\sqrt{\frac{P}{Mt}} h^T ...
0
votes
2answers
35 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 ...
4
votes
1answer
499 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} ...
0
votes
1answer
303 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 ...
0
votes
1answer
28 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 ...
3
votes
3answers
5k 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 ...
-1
votes
1answer
36 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 ...
0
votes
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 ...
