Hamming Error Correction with Kotlin – part 2

In this article, we continue where we left off and focus solely on error detection for Hamming codes.

https://touk.pl/blog/2017/10/17/hamming-error-correction-with-kotlin-part-1/

Error Correction

Utilizing Hamming(7,4) encoding allows us to detect double-bit errors and even correct single-bit ones!

During the encoding, we only add parity bits, so the happy path decoding scenario involves stripping the message from the parity bits which reside at known indexes (1,2,4…n, 2n):

fun stripHammingMetadata(input: EncodedString): BinaryString {
    return input.value.asSequence()
      .filterIndexed { i, _ -> (i + 1).isPowerOfTwo().not() }
      .joinToString("")
      .let(::BinaryString)
}

This is rarely the case because since we made effort to calculate parity bits, we want to leverage them first.

The codeword validation is quite intuitive if you already understand the encoding process. We simply need to recalculate all parity bits and do the parity check (check if those values match what’s in the message):

private fun indexesOfInvalidParityBits(input: EncodedString): List<Int> {
    fun toValidationResult(it: Int, input: EncodedString): Pair<Int, Boolean> =
      helper.parityIndicesSequence(it - 1, input.length)
        .map { v -> input[v].toBinaryInt() }
        .fold(input[it - 1].toBinaryInt()) { a, b -> a xor b }
        .let { r -> it to (r == 0) }

    return generateSequence(1) { it * 2 }
      .takeWhile { it < input.length }
      .map { toValidationResult(it, input) }
      .filter { !it.second }
      .map { it.first }
      .toList()
}

If they all match, then the codeword does not contain any errors:

override fun isValid(codeWord: EncodedString) =
  indexesOfInvalidParityBits(input).isEmpty()

Now, when we already know if the message was transmitted incorrectly, we can request the sender to retransmit the message… or try to correct it ourselves.

Finding the distorted bit is as easy as summing the indexes of invalid parity bits – the result is the index of the faulty one. In order to correct the message, we can simply flip the bit:

override fun decode(codeWord: EncodedString): BinaryString =
  indexesOfInvalidParityBits(codeWord).let { result ->
      when (result.isEmpty()) {
          true -> codeWord
          false -> codeWord.withBitFlippedAt(result.sum() - 1)
      }.let { extractor.stripHammingMetadata(it) }
  }

We flip the bit using an extension:

private fun EncodedString.withBitFlippedAt(index: Int) = this[index].toString().toInt()
  .let { this.value.replaceRange(index, index + 1, ((it + 1) % 2).toString()) }
  .let(::EncodedString)

We can see that it works by writing a home-made property test:

@Test
fun shouldEncodeAndDecodeWithSingleBitErrors() = repeat(10000) {
    randomMessage().let {
        assertThat(it).isEqualTo(decoder.decode(encoder.encode(it)
          .withBitFlippedAt(rand.nextInt(it.length))))
    }
}

Unfortunately, the Hamming (7,4) does not distinguish between codewords containing one or two distorted bits. If you try to correct the two-bit error, the result will be incorrect.

Disappointing, right? This is what drove the decision to make use of an additional parity bit and create the Hamming (8,4).

Conclusion

We’ve seen how the error correction for Hamming codes look like and went through the extensive off-by-one-error workout.

Code snippets can be found on GitHub.

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Need to make a quick json fixes – JSONPath for rescue

From time to time I have a need to do some fixes in my json data. In a world of flat files I do this with grep/sed/awk tool chain. How to handle it for JSON? Searching for a solution I came across the JSONPath. It quite mature tool (from 2007) but I haven't hear about it so I decided to share my experience with others.

First of all you can try it without pain online: http://jsonpath.curiousconcept.com/. Full syntax is described at http://goessner.net/articles/JsonPath/



But also you can download python binding and run it from command line:
$ sudo apt-get install python-jsonpath-rw
$ sudo apt-get install python-setuptools
$ sudo easy_install -U jsonpath

After that you can use inside python or with simple cli wrapper:
#!/usr/bin/python
import sys, json, jsonpath

path = sys.argv[
1]

result = jsonpath.jsonpath(json.load(sys.stdin), path)
print json.dumps(result, indent=2)

… you can use it in your shell e.g. for json:
{
"store": {
"book": [
{
"category": "reference",
"author": "Nigel Rees",
"title": "Sayings of the Century",
"price": 8.95
},
{
"category": "fiction",
"author": "Evelyn Waugh",
"title": "Sword of Honour",
"price": 12.99
},
{
"category": "fiction",
"author": "Herman Melville",
"title": "Moby Dick",
"isbn": "0-553-21311-3",
"price": 8.99
},
{
"category": "fiction",
"author": "J. R. R. Tolkien",
"title": "The Lord of the Rings",
"isbn": "0-395-19395-8",
"price": 22.99
}
],
"bicycle": {
"color": "red",
"price": 19.95
}
}
}

You can print only book nodes with price lower than 10 by:
$ jsonpath '$..book[?(@.price 

Result:
[
{
"category": "reference",
"price": 8.95,
"title": "Sayings of the Century",
"author": "Nigel Rees"
},
{
"category": "fiction",
"price": 8.99,
"title": "Moby Dick",
"isbn": "0-553-21311-3",
"author": "Herman Melville"
}
]

Have a nice JSON hacking!From time to time I have a need to do some fixes in my json data. In a world of flat files I do this with grep/sed/awk tool chain. How to handle it for JSON? Searching for a solution I came across the JSONPath. It quite mature tool (from 2007) but I haven't hear about it so I decided to share my experience with others.