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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92 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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59 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
774 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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195 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
926 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
228 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 $a(50\%)$, $...
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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 ...
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2k 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
127 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
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 ...
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1answer
364 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
313 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
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{...
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1answer
192 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
391 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
808 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
153 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
70 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
229 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
59 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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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 ...
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1answer
824 views

Golay complementary sequences in 802.11ad

The Golay complementary sequences consist of two sequences of the same length $N$ such that there acyclic autocorrelation sequences have sidelobes equal in magnitude but opposite in sign. So, when the ...
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0answers
748 views

Generating LDPC codes of arbitrary sizes in MATLAB

I am having problems generating LDPC codes of arbitrary sizes in MATLAB primarily because MATLAB insists on the parity check matrix that is input into its ldpcenc ...
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1answer
456 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 ...
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37 views

What is special about the theorem that over GF(2), $f^2(X) = f(X^2)$?

What is special about the theorem that over GF(2), $f^2(X) = f(X^2)$? There is a some 10-line proof for the same in "page no.42, Shu Lin, Daniel J. Costello-Error Control Coding (2nd Edition)-...
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1answer
393 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 = ...
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1answer
145 views

How to write cyclic codes?

I am studying cyclic codes. From what I understood of it, a cyclic code is a special kind of linear code with the property that any codeword cyclic shift is also a codeword. Generally, we start with ...
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3answers
57 views

In cyclic codes, a code vector can be obtained from another by simple circular shift. Why then the other method?

In cyclic codes, a code vector can be obtained from another by simple circular shift. Why then the other method is taught that is a bit round about? Take the code polynomial. Multiply it by the ...
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1answer
76 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. ...
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729 views

Is there any formula for coding gain of Turbo code?

I want to compare throughput under different MCS( modulation and coding scheme). We know Shannon capacity $C = B \log(1+SNR)$ can be used to calculate throughput by SNR. However, there is no MCS ...
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47 views

Block code error control with $d \ge c+u+1$

This is about error control coding formula $$ d \ge c+u+1$$ of a block code, with $c$ being the number of correctable errors, $u$ being the number of uncorrectable errors, and $d$ being the ...
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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 ...
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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 ...
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1answer
861 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 ...
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1answer
365 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?
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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). ...
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84 views

Can we break the Shannon capacity? [duplicate]

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). ...
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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 ...
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1answer
716 views

Limitations of Arithmetic coding?

I have been working on an assignment for university in which I have to compress an 80K message consisting of only two symbols, 'a' and 'b', having probability values of 0.6 and 0.4. I have ...
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1answer
186 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 ...
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2answers
875 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 ...
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2answers
376 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 $[... s_0, s_1, s_2, s_3, s_4, s_5, s_6, s_7, s_8, s_9, ..., s_{100}, ...]$...
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1answer
419 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 $[1 0 1 0 \ldots]$ ...
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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 ...
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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 ...
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1answer
374 views

Viterbi Decoder - Decoding Continuously Encoded Stream Partially

I am in trouble with Viterbi decoder for a while. I have some questions. I need to decode messages from a continuous stream which is encoded without resetting the state metrics. Each message starts ...
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3answers
885 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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1answer
243 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 ...