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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16
votes
5answers
6k views

Can we break the Shannon capacity?

I have a friend working in wireless communications research. He told me that we can transmit more than one symbol in a given slot using one frequency (of course we can decode them at the receiver). ...
9
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2answers
4k views

How to soft decode DQPSK?

I'm successfully soft-decoding D-BPSK by taking the dot-product of the constellation-position of the symbol and of the previous symbol. If the result is >= 1, then the symbol phase hasn't changed and ...
5
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1answer
181 views

Does any error correction code still work in such situation?

I'm looking for a kind of error correction code or solution that can correct my codeword in this case: My message holds $k$ bits, and $2k$ bits codeword (rate is $1/2$) is produced by the generator ...
5
votes
1answer
441 views

What is the cost of Hamming coding?

We know that (7,4) hamming code has 4 message bits and 7 code bits and can detect any single bit error. The (12,4) repetition code has 4 message bits and 12 code bits and can detect any single bit ...
4
votes
3answers
879 views

Optimal DC-free line encoding

I have a block of n bits that I'd like to encode into m bits that have an equal number of zeros and ones. I looked at protocols like 8b/10b but it wastes 25% of the data to achieve balance. As an ...
4
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2answers
1k views

Why does FEC seem to make BER worse at low Eb/N0?

I've been plotting BER curves and am wondering why FEC seems to make a BER curve worse at low Eb/N0 than the un-coded theoretical BER curve? My example plot below is for Differential BPSK using a ...
4
votes
3answers
3k views

Why is an interleaver often placed between an outer block code and an inner convolution code?

It seems that when doing FEC with a concatenated-code, an interleaver is often placed between the outer block code and the inner convolution code. The explanations I've seen say that this is because ...
4
votes
1answer
228 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 ...
4
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1answer
364 views

Why is privacy scrambling a standalone block in a communications transmitter?

In some telecommunication systems, scrambling of transmitted data is applied to provide some level of security. For example, the communication system might look like: Data -> Scrambling -> ...
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 ...
4
votes
1answer
241 views

Viterbi decoder on a bit stream where the preamble is also coded

I hope this is not off-topic for this site. In my problem, Viterbi decoder is used for decoding convolutional-coded (rate = 1/2, constraint length = 7) messages. A message is 250 bits where the ...
4
votes
1answer
497 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} ...
3
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2answers
765 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, ...
3
votes
3answers
37k views

Calculate symbol rate for QAM modulation

Not sure if this is the right place to ask, feel free to move it if any other site suits this better. Anyway I am referring to QAM modulation used in US Cable TV. I know it comes under Annex B which ...
3
votes
3answers
4k 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 ...
3
votes
3answers
1k 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 ...
3
votes
2answers
1k views

Meaning of channel capacity in the AWGN channel

I understand the concept of channel capacity as the maximal rate of the channel code I can apply without making a mistake in the receiver, in that sense the capacity is between 0 and 1. What I don't ...
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 ...
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 ...
3
votes
1answer
286 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 <...
3
votes
1answer
2k views

Hamming code exercise

I'm preparing for my exams I stumbled across this exercise. Now I can't seem to figure it out. Anybody can help me ? The exercise: For the 8bit data word: 00111001 the check bits are: 0111. Now if ...
3
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0answers
187 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 ...
2
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3answers
3k 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{...
2
votes
1answer
2k views

increase of encoding rate increases bandwidth?

I came across this paragraph in an article about signal processing. Addition of redundant bits for improving the error probability leads to bandwidth expansion of the transmitted signal by an amount ...
2
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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}...
2
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1answer
856 views

Transmission capacity in “duobinary coding”

In "duo-binary signalling" how exactly is the transmission capacity increased? Because , when we encode the binary bits, the bit duration remains the same, but the amplitude will change. Then how can ...
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 ...
2
votes
1answer
115 views

Generate Minimum distance codes

I am trying to generate a set of linear block codewords of length n and have minimum hamming distance dmin. I understand Hamming codes but they are not flexible with n. One possible way I can think of ...
2
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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
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2answers
776 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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2answers
700 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 ...
1
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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, &...
1
vote
1answer
86 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 $...
1
vote
1answer
376 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. $R_m=1$ ...
1
vote
2answers
872 views

Why is a precoder necessary for DQPSK and what does it accomplish?

I've implemented a soft-decoder for DQPSK using the wonderful answers I received here: How to soft decode DQPSK? To get the soft-decoder working properly I needed to precode the data I was sending ...
1
vote
2answers
372 views

Viterbi Decoder - Symbol Alignment

With a 1/2-rate convolutional encoder, $n$ bits are encoded into $2n$ symbols. Assume we have a long encoded stream such as $[... s_0, s_1, s_2, s_3, s_4, s_5, s_6, s_7, s_8, s_9, ..., s_{100}, ...]$...
1
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1answer
911 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 ...
1
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1answer
96 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 ...
1
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1answer
303 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." ...
1
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1answer
417 views

Viterbi Decoder - How does inverting the input bits affect the result?

Does converting zeros into ones and ones into zeros in the input stream affect the decoding result? Empirically I have seen that it does not affect, decoding $[0 1 0 1 \ldots]$ and $[1 0 1 0 \ldots]$ ...
1
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1answer
559 views

determining FEC or parity bits from percent error

I am very new to signal processing and my background is in physics. I would like to know if it is possible to determine the number of parity bits needs to theoretically get 100% transmission from a ...
1
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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
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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)}...
1
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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) ...
1
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1answer
357 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'...
1
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1answer
186 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 ...
1
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1answer
362 views

Why is $x$ not considered a primitive polynomial while being considered an irreducible polynomial?

In "Shu Lin, Daniel J. Costello-Error Control Coding (2nd Edition), Prentice Hall 2004" it is given that in $GF(2)$, if $f(x)$ is an irreducible polynomial of degree $m$ it divides $x^n+1$ where $n = ...
1
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1answer
73 views

In block codes (channel coding), in practice how is the message length ($k$) fixed?

In block codes (channel coding), in practice, how is the message length ($k$) fixed? If $k$ is large, the practical implementation of it requires huge memory if look up table approach is adopted. ...
1
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1answer
364 views

Important differences between BCJR and SOVA algorithms?

BCJR algorithm needs noise variance for Gamma (branch metrices) calculation. So I am wondering does SOVA (soft output Viterbi algorithm) needs noise variance?
1
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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{...