The cell identity is a global cell ID that is used to identify the cell from a OAM perspective. The physical cell identity has a range of 0 to 503 and it is used to scramble the data to help the mobile separate information from the different transmitters. A physical cell ID will determine the primary and secondary sync signal sequence. It is similar to the Scrambling Codes from UMTS.

When an operator deploys an LTE cell, they will select a cell ID that they will use for identify the cell within their network and a physical cell ID that will be used to transmit the data over the cell. You probably get this concept at this point, but this is the example that helps me keep this strait. Let's say that we are going to deploy a LTE network in a city and that city needs 1000 cells. Each of the 1000 cells will have their own cell ID, but, since there is only 504 physical cell IDs, we will need to repeat the physical cell IDs twice. The key is that that the two cell that share a physical cell ID cannot be geographically close to each other or they will interfere will each other.

The physical cell identity and the ECGI are different things. The physical cell identity is what the physical layer used to identify and separate data coming from different transmitters. The ECGI is a system level parameter that identifies the cell. Since there is only 504 physical cell ids, they will be repeated many times in a given system (even within a given metropolitan city). The ECGI should not repeat.

Cyclic Redundancy Check http://www.relisoft.com/science/CrcMath.html

Error detection is important whenever there is a non-zero chance of your data getting corrupted. Whether it's an Ethernet packet or a file under the control of your application, you can add a piece of redundant information to validate it.

The simplest example is a parity bit. Many computers use one parity bit per byte of memory. Every time the byte gets written, the computer counts the number of non-zero bits in it. If the number is even, it sets the ninth parity bit, otherwise it clears it. When reading the byte, the computer counts the number of non-zero bits in the byte, plus the parity bit. If any of the nine bits is flipped, the sum will be odd and the computer will halt with a memory error. (Of course, if two bits are flipped--a much rarer occurrence--this system will not detect it.)

For messages longer than one byte, you'd like to store more than one bit of redundant information. You might, for instance, calculate a checksum. Just add together all the bytes in the message and append (or store somewhere else) the sum. Usually the sum is truncated to, say, 32 bits. This system will detect many types of corruption with a reasonable probability. It will, however, fail badly when the message is modified by inverting or swapping groups of bytes. Also, it will fail when you add or remove null bytes.

Calculating a Cyclic Redundancy Check is a much more robust error checking algorithm. In this article I will sketch the mathematical foundations of the CRC calculation and describe two C++ implementations--first the slow but simple one, then the more optimized one.

Polynomials

Here's a simple polynomial, 2x² - 3x + 7. It is a function of some variable x, which depends only on powers of x. The degree of a polynomial is equal to the highest power of x in it; here it is 2 because of the x² term. A polynomial is fully specified by listing its coefficients, in this case (2, -3, 7). Notice that to define a degree-d polynomial you have to specify d + 1 coefficients.

It's easy to multiply polynomials. For instance,

Conversely, it is also possible to divide polynomials. For instance, the above equation can be rewritten as a division:

Just like in integer arithmetic, one polynomial doesn't have to be divisible by another. But you can always divide out the "whole" part and be left with the remainder. For instance x² - 2x is not divisible by x + 1, but you can calculate the quotient to be x - 3 and the remainder to be 3:

In fact you can use a version of long division to perform such calculations

Arithmetic Modulo Two

Most of us are familiar with polynomials whose coefficients are real numbers. In general, however, you can define polynomials with coefficients taken from arbitrary sets. One such set (in fact a field) consists of the numbers 0 and 1 with arithmetic defined modulo 2. It means that you perform arithmetic as usual, but if you get something greater than 1 you keep only its remainder after division by 2. In particular, if you get 2, you keep 0. Here's the addition table:

The multiplication table is equally simple:

What's more, subtraction is also well defined (in fact the subtraction table is identical to the addition table) and so is division (except for division by zero). What is nice, from the point of view of computer programming, is that both addition and subtraction modulo 2 are equivalent to bitwise exclusive or (XOR).

Now imagine a polynomial whose coefficients are zeros and ones, with the rule that all arithmetic on these coefficients is performed modulo 2. You can add, subtract, multiply and divide such polynomials (they form a ring). For instance, let's do some easy multiplication:

Let's now simplify our notation by representing a polynomial as a series of coefficients. For instance, 1x² + 0x + 1 has coefficients (1, 0, 1), 1x + 1 (1, 1), and 1x³ + 1x² + 1x + 1 (1, 1, 1, 1).

Do you see what I am driving at? A polynomial with coefficients modulo 2 can be represented as a series of bits. Conversely, any series of bits can be looked upon as a polynomial. In particular any binary message, which is nothing but a series of bits, is equivalent to a polynomial.

CRC

Take a binary message and convert it to a polynomial then divide it by another predefined polynomial called the key. The remainder from this division is the CRC. Now transmit both the message and the CRC. The recipient of the transmission does the same operation (divides the message by the same key) and compares his CRC with yours. If they differ, the message must have been mangled. If, on the other hand, they are equal, the odds are pretty good that the message went through uncorrupted. Most localized corruptions (burst of errors) will be caught using this scheme.

Not all keys are equally good. The longer the key, the better error checking. On the other hand, the calculations with long keys can get pretty involved. Ethernet packets use a 32-bit CRC corresponding to degree-31 remainder (remember, you need d + 1 coefficients for a degree-d polynomial). Since the degree of the remainder is always less than the degree of the divisor, the Ethernet key must be a polynomial of degree 32. A polynomial of degree 32 has 33 coefficients requiring a 33-bit number to store it. However, since we know that the highest coefficient (in front of x³²) is 1, we don't have to store it. The key used by the Ethernet is 0x04c11db7. It corresponds to the polynomial:

There is one more trick used in packaging CRCs. First calculate the CRC for a message to which you have appended 32 zero bits. Suppose that the message had N bits, thus corresponding to degree N-1 polynomial. After appending 32 bits, it will correspond to a degree N + 31 polynomial. The top-level bit that was multiplying x^N-1 will be now multiplying x^N+31 and so on. In all, this operation is equivalent to multiplying the message polynomial by x³². If we denote the original message polynomial by M (x), the key polynomial by K (x) and the CRC by R (x) (remainder) we have:

Now add the CRC to the augmented message and send it away. When the recipient calculates the CRC for this sum, and there was no transmission error, he will get zero. That's because:

You might think I made a sign mistake--it should be -R (x) on the left. Remember, however, that in arithmetic modulo 2 addition and subtraction are the same!

管理者警言：创新是企业进步之魂——众多的管理学大师如是说。

是的，没错。任何企业每前进一步，都面临着太多的未知的风险。

企业家的核心使命就是在前路茫茫的充满了不确定性的环境中，寻觅确定性，寻求方向与突破点以及制胜的法术。因此，企业家无不具有冒险的某些特质：赌性，抗压性，以及对任何新鲜变化的亢奋。即使那些百年老店，主人代代更迭，但成功者莫不是在反叛传统的范式中而进步的。可以说，企业永续发展的秘诀就在于创新和变化。

然而，创新则意味着破坏，变革亦伴随着动荡。所以，如何把控制创新与秩序的均衡，如何拿捏变革的节奏与分寸，恰恰是企业管理的真正难点。许多情形下，萧规曹随表现了企业核子基因的传承，而创新更多的是修补。变则通，说对了一半；另一半可能是，变则溃，则死。在创新成为时髦的当今，我们还是要多一些对过度创新的警惕。

中国三十年的开放史改革史，也同时是一部无数的商界流星们纷纷升起又急急陨落的充满了悲喜色彩的历史长剧。昨日指点长空，风光无限；今日遍地黄花，一派萧索。何故也？一句话——显，则险矣！

争利于时，乃商人之本性，从商之要义；而逐名于朝，却是商人之大忌，经商之歧路。熙攘之红尘无疑有既定的角色定位，从某些意味上讲，“明星”的桂枝专属于从艺者和从政者，以及其他阶层者去攀折，唯独企业家和从商着要远离，甚至越远越好。名利不可兼得，就像从政者不得趋利，商人亦不应竞名。

三十年的中国商史，有太多的商界强人耐不住寂寞，在些许的成就和有缺憾的辉煌面前，被动的或主动的将自己置于炫目的聚光灯下，或五色杂陈的Party聚会中，去寻求飞蛾扑火的那一刹那的快感……其结果往往是，名成矣又败矣，而利亦失矣，甚或身裂也。

相反的是，那些有足够定力的孤独者，才有可能成为中国商界的孤独英雄，也有可能造就中国级世界级的相对长寿的商业帝国，也许在当下会默默无迹，但他们，很可能就是浩浩上河中的那颗恒星——相对于恒尘中的流行而言……