# Questions tagged [coding]

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The probability of the undetected errors for an n bit CRC is said to be $1/2^n$. But in practice, CRC also has bit errors in itself. Could I say that a 16 bit CRC reduces to a 13 bit CRC if the BER is ...
• 41
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### Differential value range reduction for Huffman encoding

I am trying to understand a piece of coding technology and place it in its context, but I am unable to find any literature on the subject. It would be much appreciated if someone could point me in the ...
• 1
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### Approximating variable-length coding by "aggregating" fixed-length coding

Consider the problem where I want to quantize a univariate standard Gaussian with two bits, and the objective is to minimize MSE reconstruction loss. According to these slides, the Lloyd algorithm and ...
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### Is it better to do fixed-length Lempel Ziv Encoding or variable length?

I performed variable-length LZW encoding in Matlab on a large set of text where my dictionary looks like this (size = 28): ...
1 vote
58 views

### Z-Transform of a Precoder with XOR

I am reading a paper called "Design and Comparison of Three 20-Gb/s Backplane Transceivers for Duobinary, PAM4, and NRZ Data" and got stuck on seemingly easy thing, how the Z-domain ...
67 views

### Is this an appropriate Huffman code?

The problem is question 6.25 from Proakis, Communication Systems Engineering (2001) Design a ternary Huffman code, using 0, 1, 2 as letters, for a source with output alphabet probabilities given by {...
161 views

### RS FEC correct more than t/2 errors sometimes... why is this happening?

According to the Reed-Solomon Wikipage, the RS code can correct up to $\lfloor\frac{t}{2}\rfloor$. While I was playing around with Reed-Solomon FEC (github repo), I noticed that sometimes the RS(544, ...
• 155
151 views

### What is the best coding strategy?

There is a dataset of $N$ elements, each represented by $K$ bits. Now due to hardware limitations to reduce memory for storage, they have to be reprocessed into $K'$ bits each, and $K'<K$. What is ...
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1 vote
39 views

### Minimum distance question

I´m reading a paper on Miller codes and I´m having trouble calculating the minimum distance out of a state diagram. The paper states in Fig. 3. that "it is easy to verify that dmin for these ...
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91 views

### Other Examples of Complete Orthonormal Systems

I am interested in other examples of finite and complete orthogonal basis. I am not confident in my use of the term “complete”, so what I mean specifically is a set of basis vectors that can be used ...
• 52.4k
1 vote
154 views

### Why is Line coding called "Line coding"?

Guys do you now why line coding also called digital base band modulation named "line coding" where does it come? and how is the name related to modulation
212 views

### Optimal idle or frame sync symbols for OQPSK

Okay, everyone here knows that my thing was audio and that I have never gotten paid to do anything regarding communications systems. So, while I know a thing or two about DSP and even a little about ...
173 views

### Shortened linear codes

I've been working on my linear code assignment in my coding theory course and I have encountered a problem I would like to get help with. the question is described below. I will try to expalin what I ...
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1 vote
31 views

This question may be interpreted as a second part of this other question. Basically, if we encode our data using Huffman's encoding and we want to introduce some FEC afterwards, unless we use a ...
• 157
174 views

### Having trouble interpreting z-transform description of a predictor from a codec paper

I've been looking at the opus paper (https://arxiv.org/pdf/1602.04845.pdf); in particular, in section 4.1, they describe the predictor for the current band energy based on energy from both the current ...
406 views

### Optimal FEC option for extremely low SNR situation

I am new to this site, which I joined with the aim of finding someone to help me with a little doubt. I am trying to design a system that must be able to work at extremely low (the lower, the better, ...
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1 vote
232 views

### understanding FIR SRRC filter with memory implementation in C

I translated the Matlab QPSK receiver/transmitter into real-time C code that I have running on a PlutoSDR platform. QPSK receiver/transmitter I wrote the square root raised cosine filter for the TX ...
206 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 ...
130 views

### Multi-bit gold code

Is the multi-bit gold code resulted from a xor of two different multi-bit m-sequences will still maintain its statistical property (bounded correlation, distribution of 1 and 0) ?
• 149
35 views

### How to apply an offset to a complex exponential without chopping it off?

I am trying to encode a bitstream as offset in a complex exponential, but when I do, the sinusoids get chopped off. Do I need to apply a lowpass to the bitstream or is there a more elegant way? ...
• 147
303 views

### Transition table / matrix for convolutional encoder K=3 understandings

Im trying to understand convolutional encoder $K=3$ , and I almost understand it but still confused about what's called transition matrix which in other words it means what input value ($0$ or $1$) ...
1k views

### Finding preferred pair of $m$-sequence for Gold code

I would like to find a preferred pair of $m$-sequence of degree 34 (not a multiple of 4) for Gold code. However, I am lost when I am checking William Wesley Peterson's table in his Error-correcting ...
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1 vote
1k views

### Differential Encoding for M-PSK

Confused about a few topics w.r.t. differential encoding/decoding. First, consider the below BER curve taken from wikipedia ( https://en.wikipedia.org/wiki/Phase-shift_keying ) comparing BPSK/QPSK and ...
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1 vote
58 views

### Most reliable way to decode PAM2 signal with unknown signal levels?

I assume this is pretty much a standard problem. I have a PAM2 signal that comes from a complex envelope (i.e., it is not zero-centered) and is heavily imposed by noise. This shows 20 different ...
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1 vote
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### What is the Asymptotic Equipartition Property (AEP)?

I am currently studying about Polar Codes in 5G standard and while reading my paper I found something called AEP which is required for channel coding. I surfed the web but didn't found a satisfying ...
106 views

### Prefix code of symbol pairs

An input sequence consists of two symbols, each independently and randomly chosen from a set of symbols with known associated probabilities. Each symbol is independently encoded using a prefix code ...
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38 views

### Randomized prefix code

An input symbol is randomly chosen from a set of symbols with known associated probabilities and encoded using a prefix code that minimizes the expected codeword length. Is it possible to further ...
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